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## Miranville, Alain M.

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 Author ID: miranville.alain-m Published as: Miranville, A.; Miranville, Alain; Miranville, Alain M. Homepage: http://wwwmathlabo.univ-poitiers.fr/~miranv/ External Links: MGP · dblp
 Documents Indexed: 230 Publications since 1993, including 13 Books
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#### Co-Authors

 52 single-authored 23 Cherfils, Laurence 23 Gatti, Stefania 21 Zelik, Sergey V. 19 Quintanilla de Latorre, Ramón 17 Grasselli, Maurizio 11 Efendiev, Messoud 11 Schimperna, Giulio 10 Pata, Vittorino 9 Conti, Monica C. 8 Temam, Roger Meyer 7 Piétrus, Alain 6 Gal, Ciprian Gheorghe Sorin 6 Peng, Shuiran 5 Chepyzhov, Vladimir V. 5 Fakih, Hussein 5 Guillevin, Rémy 5 Makki, Ahmad 5 Moroşanu, Costică 5 Rakotoson, Jean-Michel 4 Bonfoh, Ahmed S. 4 Carrive, Maïté 4 Fabrie, Pierre 4 Galusinski, Cédric 4 Henrot, Antoine 4 Perrillat-Mercerot, Angélique 4 Saoud, Wafa 3 Guillevin, Carole 3 Magaña, Antonio 3 Ruiz Goldstein, Giséle 3 Talhouk, Raafat 2 Alaa, Noureddine 2 Aouadi, Moncef 2 Bourmeyster, Nicolas 2 Dambrine, Marc 2 Deheuvels, Thibaut 2 Fragnelli, Genni 2 Gilardi, Gianni 2 Giorgini, Andrea 2 Israel, Haydi 2 Laamri, El Haj 2 Muresan, Adrian C. 2 Petcu, Madalina 2 Rocca, Elisabetta 2 Roche, Jean Rodolphe 2 Schmitt, Didier 2 Wang, Xiaoming 2 Zhang, Wen 1 Alsayed, Hawraa 1 Andami Ovono, Armel 1 Aziz-Alaoui, Moulay-Ahmed 1 Barbu, Tudor 1 Belinsky, Boris P. 1 Bosia, Stefano 1 Cantin, Guillaume 1 Cârjă, Ovidiu 1 Cavaterra, Cecilia 1 Chehab, Jean-Paul 1 Chen, Min 1 Dell’Oro, Filippo 1 Dubois, Thomas 1 Eden, Alp 1 Goldstein, Jerome Arthur 1 Hnid, Mohammed 1 Hou, Xiaojie 1 Ilyin, Alexei A. 1 Kalantarov, Varga K. 1 Lan, Kunquan 1 Langa, Jose’ Antonio 1 Li, Lu 1 Lichnewsky, Alain 1 Lods, Véronique 1 Lorenzi, Luca 1 Lu, Xin 1 Mininni, Rosa Maria 1 Naudin, Mathieu 1 Ntsokongo, Armel Judice 1 Qin, Yuming 1 Real Anguas, José 1 Romanelli, Silvia 1 Rossi, Riccarda 1 Rougirel, Arnaud 1 Ruget, Claudine 1 Saad, Mazen 1 Sadaka, Georges 1 Segatti, Antonio 1 Shivaji, Ratnasingham 1 Showalter, Ralph E. 1 Stefanelli, Ulisse 1 Su, Jianzhong 1 Titi, Edriss Saleh 1 Truskinovsky, Lev 1 Visintin, Augusto 1 Wang, Rongnian 1 Wang, Xiuqing 1 Wehbe, Ali 1 Wehbe, Charbel 1 Wu, Hao 1 Xu, Chuanju 1 Yan, Xingjie 1 Yang, Xinguang ...and 4 more Co-Authors
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#### Serials

 17 Discrete and Continuous Dynamical Systems 17 Discrete and Continuous Dynamical Systems. Series S 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 9 Communications on Pure and Applied Analysis 8 Mathematical Methods in the Applied Sciences 8 Applied Mathematics Letters 8 Asymptotic Analysis 7 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 6 Applicable Analysis 6 Journal of Mathematical Analysis and Applications 6 Nonlinear Analysis. Real World Applications 5 Discrete and Continuous Dynamical Systems. Series B 5 Journal of Applied Analysis and Computation 3 Nonlinearity 3 Mathematische Nachrichten 3 Quarterly of Applied Mathematics 3 Physica D 3 Applications of Mathematics 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Advances in Mathematical Sciences and Applications 3 Electronic Journal of Differential Equations (EJDE) 3 Mediterranean Journal of Mathematics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Applied Mathematics and Optimization 2 Differential and Integral Equations 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 NoDEA. Nonlinear Differential Equations and Applications 2 Journal of Mathematical Study 2 Journal of Evolution Equations 2 Milan Journal of Mathematics 2 Central European Journal of Mathematics 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 AIMS Mathematics 1 IMA Journal of Applied Mathematics 1 International Journal of Engineering Science 1 Rocky Mountain Journal of Mathematics 1 Bulletin of Mathematical Biology 1 Applied Mathematics and Computation 1 Hokkaido Mathematical Journal 1 Indiana University Mathematics Journal 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Proceedings of the American Mathematical Society 1 Ricerche di Matematica 1 Chinese Annals of Mathematics. Series B 1 Applied Numerical Mathematics 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Applied Mathematical Modelling 1 Communications in Partial Differential Equations 1 SIAM Journal on Mathematical Analysis 1 Journal of Mathematical Imaging and Vision 1 Journal of Nonlinear Science 1 Continuum Mechanics and Thermodynamics 1 Revue d’Analyse Numérique et de Théorie de l’Approximation 1 Topological Methods in Nonlinear Analysis 1 Calculus of Variations and Partial Differential Equations 1 Russian Journal of Mathematical Physics 1 Journal of Mathematical Sciences (New York) 1 Nonlinear World 1 Computational and Applied Mathematics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales (España) 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Electronic Journal of Qualitative Theory of Differential Equations 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Journal of Applied Mathematics 1 Multiscale Modeling & Simulation 1 Communications in Mathematical Sciences 1 Analysis and Applications (Singapore) 1 Cubo 1 Mathematical Biosciences and Engineering 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Inverse Problems and Imaging 1 AIMS Series on Differential Equations and Dynamical Systems 1 SIAM Journal on Imaging Sciences 1 Electronic Research Announcements in Mathematical Sciences 1 Bulletin of the Transilvania University of Braşov. Series III. Mathematics, Informatics, Physics 1 Annals of the University of Bucharest. Mathematical Series 1 Evolution Equations and Control Theory 1 Advances in Nonlinear Analysis 1 Nonlinear Analysis. Theory, Methods & Applications 1 Journal of Elliptic and Parabolic Equations 1 Electronic Research Archive
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#### Fields

 205 Partial differential equations (35-XX) 45 Dynamical systems and ergodic theory (37-XX) 44 Classical thermodynamics, heat transfer (80-XX) 34 Mechanics of deformable solids (74-XX) 29 Fluid mechanics (76-XX) 16 General and overarching topics; collections (00-XX) 11 Numerical analysis (65-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Operator theory (47-XX) 7 Biology and other natural sciences (92-XX) 5 Ordinary differential equations (34-XX) 4 History and biography (01-XX) 4 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Computer science (68-XX) 3 Information and communication theory, circuits (94-XX) 2 Optics, electromagnetic theory (78-XX) 1 Real functions (26-XX) 1 Probability theory and stochastic processes (60-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

182 Publications have been cited 2,237 times in 814 Documents Cited by Year
Attractors for dissipative partial differential equations in bounded and unbounded domains. Zbl 1221.37158
Miranville, A.; Zelik, S.
2008
Exponential attractors for a nonlinear reaction-diffusion system in $$\mathbb R^3$$. Zbl 1151.35315
Efendiev, Messoud; Miranville, Alain; Zelik, Sergey
2000
Uniform exponential attractors for a singularly perturbed damped wave equation. Zbl 1060.35011
Fabrie, Pierre; Galusinski, Cedric; Miranville, Alain; Zelik, Sergey
2004
The Cahn-Hilliard equation with logarithmic potentials. Zbl 1250.35129
Cherfils, Laurence; Miranville, Alain; Zelik, Sergey
2011
Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Zbl 1050.35113
Miranville, Alain; Zelik, Sergey
2004
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions. Zbl 1172.35417
Gilardi, Gianni; Miranville, A.; Schimperna, Giulio
2009
Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. Zbl 1088.37005
Efendiev, M.; Zelik, S.; Miranville, A.
2005
Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions. Zbl 1068.35020
Miranville, A.; Zelik, S.
2005
Exponential attractors for a singularly perturbed Cahn-Hilliard system. Zbl 1046.37047
Efendiev, Messoud; Miranville, Alain; Zelik, Sergey
2004
The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Zbl 1203.35046
Miranville, Alain; Zelik, Sergey
2010
On the Caginalp system with dynamic boundary conditions and singular potentials. Zbl 1212.35012
Cherfils, Laurence; Miranville, Alain
2009
The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials. Zbl 1194.35074
Grasselli, Maurizio; Miranville, Alain; Schimperna, Giulio
2010
Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials. Zbl 1133.35017
Grasselli, Maurizio; Miranville, Alain; Pata, Vittorino; Zelik, Sergey
2007
Hyperbolic relaxation of the viscous Cahn-Hilliard equation in 3-D. Zbl 1073.35043
Gatti, Stefania; Grasselli, Maurizio; Pata, Vittorino; Miranville, Alain
2005
Long time behavior of the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions. Zbl 1223.35067
Gilardi, Gianni; Miranville, Alain; Schimperna, Giulio
2010
Mathematical modelling in continuum mechanics. 2nd ed. Zbl 1077.76001
Temam, Roger; Miranville, Alain M.
2005
Some results on the asymptotic behavior of the Caginalp system with singular potentials. Zbl 1145.35042
Cherfils, Laurence; Miranville, Alain
2007
On the hyperbolic relaxation of the one-dimensional Cahn–Hilliard equation. Zbl 1160.35518
Gatti, Stefania; Grasselli, Maurizio; Miranville, Alain; Pata, Vittorino
2005
Robust exponential attractors for singularly perturbed phase-field type equations. Zbl 1004.35024
Miranville, Alain; Zelik, Sergey
2002
A Cahn-Hilliard model in a domain with non-permeable walls. Zbl 1228.35051
Goldstein, Gisèle Ruiz; Miranville, Alain; Schimperna, Giulio
2011
Pullback exponential attractors. Zbl 1303.37032
Langa, José A.; Miranville, Alain; Real, José
2010
Some generalizations of the Caginalp phase-field system. Zbl 1178.35194
Miranville, Alain; Quintanilla, Ramon
2009
A generalization of the Caginalp phase-field system based on the Cattaneo law. Zbl 1167.35304
Miranville, Alain; Quintanilla, Ramon
2009
A construction of a robust family of exponential attractors. Zbl 1078.37047
Gatti, Stefania; Grasselli, Maurizio; Miranville, Alain; Pata, Vittorino
2006
A variational approach to a Cahn-Hilliard model in a domain with nonpermeable walls. Zbl 1276.49014
Cherfils, L.; Gatti, S.; Miranville, A.
2013
Asymptotic behavior of a phase-field system with dynamic boundary conditions. Zbl 1123.35310
Gatti, Stefania; Miranville, Alain
2006
Small viscosity sharp estimates for the global attractor of the 2D damped-driven Navier-Stokes equations. Zbl 1084.35058
Ilyin, A. A.; Miranville, A.; Titi, E. S.
2004
A type III phase-field system with a logarithmic potential. Zbl 1213.35187
Miranville, Alain; Quintanilla, Ramon
2011
A phase-field model based on a three-phase-lag heat conduction. Zbl 1213.35111
Miranville, Alain; Quintanilla, Ramon
2011
Uniform global attractors for non-isothermal viscous and non-viscous Cahn-Hilliard equations with dynamic boundary conditions. Zbl 1183.35052
Gal, Ciprian G.; Miranville, Alain
2009
The Cahn-Hilliard equation for deformable elastic continua. Zbl 0987.35156
Carrive, M.; Miranville, A.; Piétrus, A.
2000
Cahn-Hilliard-Navier-Stokes systems with moving contact lines. Zbl 1372.35140
Gal, C. G.; Grasselli, Maurizio; Miranville, Alain
2016
Attractors for semi-linear equations of viscoelasticity with very low dissipation. Zbl 1179.35070
Gatti, S.; Miranville, A.; Pata, V.; Zelik, S.
2008
On a generalized Cahn-Hilliard equation with biological applications. Zbl 1304.35133
Cherfils, Laurence; Miranville, Alain; Zelik, Sergey
2014
Continuous families of exponential attractors for singularly perturbed equations with memory. Zbl 1196.35054
Gatti, Stefania; Miranville, Alain; Pata, Vittorino; Zelik, Sergey
2010
Some mathematical models in phase transition. Zbl 1275.35048
Miranville, Alain
2014
Asymptotic behavior of the Cahn-Hilliard-Oono equation. Zbl 1304.35342
Miranville, Alain
2011
Nonisothermal Allen-Cahn equations with coupled dynamic boundary conditions. Zbl 1178.35076
Gal, Ciprian; Grasselli, Maurizio; Miranville, Alain
2008
Exponential attractors for singularly perturbed damped wave equations: a simple construction. Zbl 1139.35030
Miranville, Alain; Pata, Vittorino; Zelik, Sergey
2007
Exponential attractors for nonautonomous first-order evolution equations. Zbl 0980.34051
Fabrie, Pierre; Miranville, Alain
1998
Asymptotic behavior of a sixth-order Cahn-Hilliard system. Zbl 1286.35047
Miranville, Alain
2014
Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potentials. Zbl 1143.35070
Cherfils, Laurence; Gatti, Stefania; Miranville, Alain
2008
Memory relaxation of first order evolution equations. Zbl 1181.35026
Gatti, Stefania; Grasselli, Maurizio; Miranville, Alain; Pata, Vittorino
2005
Some generalizations of the Cahn-Hilliard equation. Zbl 0953.35055
Miranville, Alain
2000
The Cahn-Hilliard equation. Recent advances and applications. Zbl 1446.35001
Miranville, Alain
2019
On the Bertozzi-Esedoglu-Gillette-Cahn-Hilliard equation with logarithmic nonlinear terms. Zbl 1381.35082
Cherfils, Laurence; Fakih, Hussein; Miranville, Alain
2015
Phase-field systems with nonlinear coupling and dynamic boundary conditions. Zbl 1184.35053
Cavaterra, Cecilia; Gal, Ciprian G.; Grasselli, Maurizio; Miranville, Alain
2010
Upper bound on the dimension of the attractor for nonhomogeneous Navier-Stokes equations. Zbl 0949.35112
Miranville, Alain; Wang, Xiaoming
1996
On the long time behavior of a tumor growth model. Zbl 1416.35279
Miranville, Alain; Rocca, Elisabetta; Schimperna, Giulio
2019
The Cahn-Hilliard-Oono equation with singular potential. Zbl 1386.35023
Giorgini, Andrea; Grasselli, Maurizio; Miranville, Alain
2017
A Cahn-Hilliard-Gurtin model with dynamic boundary conditions. Zbl 1277.35202
Goldstein, Gisèle Ruiz; Miranville, Alain
2013
Finite-dimensional attractors for reaction-diffusion equations in $$\mathbb{R}^n$$ with a strong nonlinearity. Zbl 0959.35025
Efendiev, Messoud; Miranville, Alain
1999
Exponential decay in one-dimensional type III thermoelasticity with voids. Zbl 1415.35259
Miranville, Alain; Quintanilla, Ramón
2019
The Cahn-Hilliard equation and some of its variants. Zbl 1425.35086
Miranville, Alain
2017
Finite-dimensional attractors for the Bertozzi-Esedoglu-Gillette-Cahn-Hilliard equation in image inpainting. Zbl 06398723
Cherfils, Laurence; Fakih, Hussein; Miranville, Alain
2015
Asymptotic behaviour of a generalized Cahn-Hilliard equation with a proliferation term. Zbl 06190759
Miranville, Alain
2013
On the conserved phase-field model. Zbl 1308.35125
Miranville, Alain
2013
On Cahn-Hilliard-Gurtin equations. Zbl 1042.74553
Bonfoh, Ahmed; Miranville, Alain
2001
Singularly perturbed 1D Cahn-Hilliard equation revisited. Zbl 1387.35341
Bonfoh, Ahmed; Grasselli, Maurizio; Miranville, Alain
2010
Robust exponential attractors for singularly perturbed phase-field equations with dynamic boundary conditions. Zbl 1180.35119
Gal, Ciprian G.; Grasselli, Maurizio; Miranville, Alain
2008
On trajectory and global attractors for semilinear heat equations with fading memory. Zbl 1186.37092
Chepyzhov, V. V.; Miranville, A.
2006
Nonisothermal phase separation based on a microforce balance. Zbl 1140.80388
Miranville, Alain; Schimperna, Giulio
2005
Mathematical modelling in continuum mechanics. Zbl 0993.76002
Temam, Roger; Miranville, Alain
2001
A model of Cahn-Hilliard equation based on a microforce balance. Zbl 0932.35118
Miranville, Alain
1999
Dynamical aspect of a generalized Cahn-Hilliard equation based on a microforce balance. Zbl 0936.35036
Miranville, A.; Piétrus, A.; Rakotoson, J. M.
1998
A generalization of the Allen-Cahn equation. Zbl 1320.35346
Miranville, Alain; Quintanilla, Ramon
2015
Analysis of the Cahn-Hilliard equation with a chemical potential dependent mobility. Zbl 1241.35024
Grasselli, Maurizio; Miranville, Alain; Rossi, Riccarda; Schimperna, Giulio
2011
Trajectory and global attractors for evolution equations with memory. Zbl 1082.35035
Chepyzhov, V. V.; Gatti, S.; Grasselli, M.; Miranville, A.; Pata, V.
2006
Infinite dimensional exponential attractors for a non-autonomous reaction-diffusion system. Zbl 1025.37043
Efendiev, Messoud; Miranville, Alain; Zelik, Sergey
2003
Long-time behavior of some models of Cahn-Hilliard equations in deformable continua. Zbl 0989.35066
Miranville, Alain
2001
Attractors for nonautonomous nonhomogeneous Navier-Stokes equations. Zbl 0908.35098
Miranville, A.; Wang, X.
1997
Incremental unknowns in finite differences in three space dimensions. Zbl 0841.65089
Chen, Min; Miranville, A.; Temam, Roger
1995
Uniqueness and regularity for the Navier-Stokes-Cahn-Hilliard System. Zbl 1419.35160
Giorgini, Andrea; Miranville, Alain; Temam, Roger
2019
Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation. Zbl 1072.35045
Efendiev, M.; Miranville, A.; Zelik, S.
2004
Consistent models of Cahn-Hilliard-Gurtin equations with Neumann boundary conditions. Zbl 0999.74007
Miranville, Alain
2001
Higher-order Cahn-Hilliard equations with dynamic boundary conditions. Zbl 1366.35062
Mininni, Rosa Maria; Miranville, Alain; Romanelli, Silvia
2017
A Cahn-Hilliard system with a fidelity term for color image inpainting. Zbl 1381.94014
Cherfils, Laurence; Fakih, Hussein; Miranville, Alain
2016
Sixth-order Cahn-Hilliard systems with dynamic boundary conditions. Zbl 1323.35093
Miranville, Alain
2015
On the longtime behavior of a 2D hydrodynamic model for chemically reacting binary fluid mixtures. Zbl 1292.35056
Bosia, Stefano; Grasselli, Maurizio; Miranville, Alain
2014
Inertial manifolds for a singular perturbation of the viscous Cahn-Hilliard-Gurtin equation. Zbl 1211.35054
Bonfoh, Ahmed; Grasselli, Maurizio; Miranville, Alain
2010
On a doubly nonlinear Cahn-Hilliard-Gurtin system. Zbl 1203.35045
Miranville, Alain; Schimperna, Giulio
2010
Doubly nonlinear Cahn-Hilliard-Gurtin equations. Zbl 1191.35068
Miranville, A.; Zelik, S.
2009
Robust exponential attractors and convergence to equilibria for non-isothermal Cahn-Hilliard equations with dynamic boundary conditions. Zbl 1173.35026
Gal, Ciprian G.; Miranville, Alain
2009
Long time behavior of a singular perturbation of the viscous Cahn-Hilliard-Gurtin equation. Zbl 1145.35011
Bonfoh, Ahmed; Grasselli, Maurizio; Miranville, Alain
2008
The dimension of the global attractor for dissipative reaction-diffusion systems. Zbl 1041.37039
Efendiev, M.; Miranville, A.
2003
Incremental unknowns on nonuniform meshes. Zbl 0913.65088
Chehab, J.-P.; Miranville, A.
1998
Exponential decay in one-dimensional type II thermoviscoelasticity with voids. Zbl 1439.35071
Miranville, Alain; Quintanilla, Ramón
2020
A Caginalp phase-field system based on type III heat conduction with two temperatures. Zbl 1338.35233
Miranville, Alain; Quintanilla, Ramon
2016
Sixth-order Cahn-Hilliard equations with singular nonlinear terms. Zbl 1332.35149
Miranville, Alain
2015
Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions. Zbl 1244.35067
Conti, Monica; Gatti, Stefania; Miranville, Alain
2012
Global solution to a phase transition model based on a microforce balance. Zbl 1074.35050
Miranville, Alain; Schimperna, Giulio
2005
Global and exponential attractors for nonlinear reaction-diffusion systems in unbounded domains. Zbl 1149.37328
Efendiev, M.; Miranville, A.; Zelik, S.
2004
Generalized Cahn-Hilliard equations with a logarithmic free energy. Zbl 1002.35062
Cherfils, L.; Miranville, A.
2000
On the dimension of the attractor for the Bénard problem with free surfaces. Zbl 0910.35148
Miranville, A.; Ziane, M.
1997
Higher-order anisotropic models in phase separation. Zbl 1422.35109
Cherfils, Laurence; Miranville, Alain; Peng, Shuiran
2019
A complex version of the Cahn-Hilliard equation for grayscale image inpainting. Zbl 1377.35143
Cherfils, Laurence; Fakih, Hussein; Miranville, Alain
2017
On the Cahn-Hilliard-Oono-Navier-Stokes equations with singular potentials. Zbl 1349.35171
Miranville, Alain; Temam, Roger
2016
Existence of solutions for anisotropic Cahn-Hilliard and Allen-Cahn systems in higher space dimensions. Zbl 1346.35029
2016
Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory. Zbl 1343.35036
2015
Well-posedness for one-dimensional anisotropic Cahn-Hilliard and Allen-Cahn systems. Zbl 1334.35106
2015
A coupled Cahn-Hilliard model for the proliferative-to-invasive transition of hypoxic glioma cells. Zbl 07333609
Li, Lu; Miranville, Alain; Guillevin, Rémy
2021
Exponential decay in one-dimensional type II thermoviscoelasticity with voids. Zbl 1439.35071
Miranville, Alain; Quintanilla, Ramón
2020
Exponential decay of solutions in type II porous-thermo-elasticity with quasi-static microvoids. Zbl 1453.35167
Magaña, A.; Miranville, A.; Quintanilla, R.
2020
Long-time behavior of the Cahn-Hilliard equation with dynamic boundary condition. Zbl 1443.35054
Miranville, Alain; Wu, Hao
2020
The Cahn-Hilliard equation. Recent advances and applications. Zbl 1446.35001
Miranville, Alain
2019
On the long time behavior of a tumor growth model. Zbl 1416.35279
Miranville, Alain; Rocca, Elisabetta; Schimperna, Giulio
2019
Exponential decay in one-dimensional type III thermoelasticity with voids. Zbl 1415.35259
Miranville, Alain; Quintanilla, Ramón
2019
Uniqueness and regularity for the Navier-Stokes-Cahn-Hilliard System. Zbl 1419.35160
Giorgini, Andrea; Miranville, Alain; Temam, Roger
2019
Higher-order anisotropic models in phase separation. Zbl 1422.35109
Cherfils, Laurence; Miranville, Alain; Peng, Shuiran
2019
On the time decay in phase-lag thermoelasticity with two temperatures. Zbl 1428.74057
Magaña, Antonio; Miranville, Alain; Quintanilla, Ramón
2019
Existence of solutions to a Cahn-Hilliard type equation with a logarithmic nonlinear term. Zbl 1409.35110
Miranville, Alain
2019
Mathematical analysis of a model for proliferative-to-invasive transition of hypoxic glioma cells. Zbl 1434.35253
Conti, Monica; Gatti, Stefania; Miranville, Alain
2019
On the Cahn-Hilliard/Allen-Cahn equations with singular potentials. Zbl 1420.35118
Miranville, Alain; Saoud, Wafa; Talhouk, Raafat
2019
Finite difference scheme for 2D parabolic problem modelling electrostatic micro-electromechanical systems. Zbl 1427.78025
Alsayed, Hawraa; Fakih, Hussein; Miranville, Alain; Wehbe, Ali
2019
Analysis of a mathematical model for the glutamate/glutamine cycle in the brain. Zbl 1427.92036
Perrillat-Mercerot, A.; Bourmeyster, N.; Guillevin, C.; Miranville, A.; Guillevin, R.
2019
Analysis of a mathematical model for brain lactate kinetics. Zbl 1406.92082
Guillevin, Carole; Guillevin, Rémy; Miranville, Alain; Perrillat-Mercerot, Angélique
2018
On the stability in phase-lag heat conduction with two temperatures. Zbl 1457.80005
Magaña, Antonio; Miranville, Alain; Quintanilla, Ramón
2018
Asymptotic behavior of higher-order Navier-Stokes-Cahn-Hilliard systems. Zbl 1394.35227
Cherfils, Laurence; Gatti, Stefania; Miranville, Alain
2018
On higher-order anisotropic conservative Caginalp phase-field systems. Zbl 1388.35089
Miranville, Alain
2018
The Cahn-Hilliard-Oono equation with singular potential. Zbl 1386.35023
Giorgini, Andrea; Grasselli, Maurizio; Miranville, Alain
2017
The Cahn-Hilliard equation and some of its variants. Zbl 1425.35086
Miranville, Alain
2017
Higher-order Cahn-Hilliard equations with dynamic boundary conditions. Zbl 1366.35062
Mininni, Rosa Maria; Miranville, Alain; Romanelli, Silvia
2017
A complex version of the Cahn-Hilliard equation for grayscale image inpainting. Zbl 1377.35143
Cherfils, Laurence; Fakih, Hussein; Miranville, Alain
2017
A singular reaction-diffusion equation associated with brain lactate kinetics. Zbl 1365.35072
Miranville, Alain
2017
Asymptotic behavior of a model for order-disorder and phase separation. Zbl 1379.35249
Miranville, Alain; Saoud, Wafa; Talhouk, Raafat
2017
On a Caginalp phase-field system with two temperatures and memory. Zbl 1372.35047
Conti, M.; Gatti, S.; Miranville, A.; Quintanilla, R.
2017
On a reaction-diffusion system associated with brain lactate kinetics. Zbl 1357.35188
Guillevin, Rémy; Miranville, Alain; Perrillat-Mercerot, Angélique
2017
Higher-order generalized Cahn-Hilliard equations. Zbl 1413.35249
Cherfils, Laurence; Miranville, Alain; Peng, Shuiran; Zhang, Wen
2017
Mathematical analysis of a parabolic-elliptic model for brain lactate kinetics. Zbl 1390.35157
Miranville, Alain
2017
A phase-field system with two temperatures and memory. Zbl 1424.35057
Conti, Monica; Gatti, Stefania; Miranville, Alain
2017
On the spatial behavior in two-temperature generalized thermoelastic theories. Zbl 1378.35299
Miranville, Alain; Quintanilla, Ramon
2017
Cahn-Hilliard-Navier-Stokes systems with moving contact lines. Zbl 1372.35140
Gal, C. G.; Grasselli, Maurizio; Miranville, Alain
2016
A Cahn-Hilliard system with a fidelity term for color image inpainting. Zbl 1381.94014
Cherfils, Laurence; Fakih, Hussein; Miranville, Alain
2016
A Caginalp phase-field system based on type III heat conduction with two temperatures. Zbl 1338.35233
Miranville, Alain; Quintanilla, Ramon
2016
On the Cahn-Hilliard-Oono-Navier-Stokes equations with singular potentials. Zbl 1349.35171
Miranville, Alain; Temam, Roger
2016
Existence of solutions for anisotropic Cahn-Hilliard and Allen-Cahn systems in higher space dimensions. Zbl 1346.35029
2016
On the phase-field-crystal model with logarithmic nonlinear terms. Zbl 1336.35086
Miranville, Alain
2016
Higher-order Allen-Cahn models with logarithmic nonlinear terms. Zbl 1364.35363
Cherfils, Laurence; Miranville, Alain; Peng, Shuiran
2016
Higher-order anisotropic Caginalp phase-field systems. Zbl 1362.35052
Miranville, Alain
2016
On the Caginalp phase-field systems with two temperatures and the Maxwell-Cattaneo law. Zbl 1348.35102
Miranville, Alain; Quintanilla, Ramon
2016
Analysis of an iterative scheme of fractional steps type associated to the nonlinear phase-field equation with non-homogeneous dynamic boundary conditions. Zbl 1353.65094
Miranville, Alain; Moroşanu, Costică
2016
On the existence, uniqueness and regularity of solutions to the phase-field transition system with non-homogeneous Cauchy-Neumann and nonlinear dynamic boundary conditions. Zbl 1443.35061
Miranville, Alain; Moroşanu, Costică
2016
On the Caginalp phase-field system based on the Cattaneo law with nonlinear coupling. Zbl 1427.35111
Andami Ovono, Armel; Miranville, Alain
2016
On the anisotropic Caginalp phase-field system with singular nonlinear terms. Zbl 1348.35097
Miranville, Alain
2016
On the Bertozzi-Esedoglu-Gillette-Cahn-Hilliard equation with logarithmic nonlinear terms. Zbl 1381.35082
Cherfils, Laurence; Fakih, Hussein; Miranville, Alain
2015
Finite-dimensional attractors for the Bertozzi-Esedoglu-Gillette-Cahn-Hilliard equation in image inpainting. Zbl 06398723
Cherfils, Laurence; Fakih, Hussein; Miranville, Alain
2015
A generalization of the Allen-Cahn equation. Zbl 1320.35346
Miranville, Alain; Quintanilla, Ramon
2015
Sixth-order Cahn-Hilliard systems with dynamic boundary conditions. Zbl 1323.35093
Miranville, Alain
2015
Sixth-order Cahn-Hilliard equations with singular nonlinear terms. Zbl 1332.35149
Miranville, Alain
2015
Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory. Zbl 1343.35036
2015
Well-posedness for one-dimensional anisotropic Cahn-Hilliard and Allen-Cahn systems. Zbl 1334.35106
2015
On the existence, uniqueness and regularity of solutions to the phase-field system with a general regular potential and a general class of nonlinear and non-homogeneous boundary conditions. Zbl 1304.35167
Cârjă, Ovidiu; Miranville, Alain; Moroşanu, Costică
2015
Smooth attractor for a nonlinear thermoelastic diffusion thin plate based on Gurtin-Pipkin’s model. Zbl 1333.35270
2015
Numerical analysis of a Cahn-Hilliard type equation with dynamic boundary conditions. Zbl 1320.65142
Israel, Haydi; Miranville, Alain; Petcu, Madalina
2015
A generalized Cahn-Hilliard equation with logarithmic potentials. Zbl 1335.35098
Miranville, Alain
2015
Multi-component Cahn-Hilliard systems with dynamic boundary conditions. Zbl 1350.35153
Conti, Monica; Gatti, Stefania; Miranville, Alain
2015
A reformulation of the Caginalp phase-field system based on the Maxwell-Cattaneo law. Zbl 1423.82023
Miranville, Alain
2015
On a generalized Cahn-Hilliard equation with biological applications. Zbl 1304.35133
Cherfils, Laurence; Miranville, Alain; Zelik, Sergey
2014
Some mathematical models in phase transition. Zbl 1275.35048
Miranville, Alain
2014
Asymptotic behavior of a sixth-order Cahn-Hilliard system. Zbl 1286.35047
Miranville, Alain
2014
On the longtime behavior of a 2D hydrodynamic model for chemically reacting binary fluid mixtures. Zbl 1292.35056
Bosia, Stefano; Grasselli, Maurizio; Miranville, Alain
2014
The Penrose-Fife phase-field model. Zbl 1304.35361
Miranville, Alain; Rocca, Elisabetta; Schimperna, Giulio; Segatti, Antonio
2014
Asymptotic behavior of the conserved Caginalp phase-field system based on the Maxwell-Cattaneo law. Zbl 1304.35123
Miranville, Alain
2014
A variational approach to a Cahn-Hilliard model in a domain with nonpermeable walls. Zbl 1276.49014
Cherfils, L.; Gatti, S.; Miranville, A.
2013
A Cahn-Hilliard-Gurtin model with dynamic boundary conditions. Zbl 1277.35202
Goldstein, Gisèle Ruiz; Miranville, Alain
2013
Asymptotic behaviour of a generalized Cahn-Hilliard equation with a proliferation term. Zbl 06190759
Miranville, Alain
2013
On the conserved phase-field model. Zbl 1308.35125
Miranville, Alain
2013
Attractors for a Caginalp model with a logarithmic potential and coupled dynamic boundary conditions. Zbl 1282.35080
Conti, Monica; Gatti, Stefania; Miranville, Alain
2013
A generalization of the Caginalp phase-field system with Neumann boundary conditions. Zbl 1288.35289
Conti, Monica; Gatti, Stefania; Miranville, Alain
2013
Existence of solutions for a one-dimensional Allen-Cahn equation. Zbl 1292.35154
Miranville, Alain
2013
Spatial decay for several phase-field models. Zbl 1433.76169
Miranville, Alain; Quintanilla, Ramon
2013
Asymptotic behavior of a generalization of the Caginalp phase-field system. Zbl 1284.35434
Conti, Monica; Dell’Oro, Filippo; Miranville, Alain
2013
A generalized conserved phase-field system based on type III heat conduction. Zbl 1288.35102
Miranville, Alain
2013
Well-posedness and long time behavior of a perturbed Cahn-Hilliard system with regular potentials. Zbl 1295.35113
Israel, Haydi; Miranville, Alain; Petcu, Madalina
2013
A conserved phase-field system based on the Maxwell-Cattaneo law. Zbl 1261.35045
Miranville, Alain; Quintanilla, Ramon
2013
Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions. Zbl 1244.35067
Conti, Monica; Gatti, Stefania; Miranville, Alain
2012
On a phase-field system based on the Cattaneo law. Zbl 1237.35089
Miranville, Alain; Quintanilla, Ramon
2012
Long time behavior of the Caginalp system with singular potentials and dynamic boundary conditions. Zbl 1267.35032
Cherfils, Laurence; Gatti, Stefania; Miranville, Alain
2012
On a phase-field model with a logarithmic nonlinearity. Zbl 1265.35139
Miranville, Alain
2012
The Cahn-Hilliard equation with logarithmic potentials. Zbl 1250.35129
Cherfils, Laurence; Miranville, Alain; Zelik, Sergey
2011
A Cahn-Hilliard model in a domain with non-permeable walls. Zbl 1228.35051
Goldstein, Gisèle Ruiz; Miranville, Alain; Schimperna, Giulio
2011
A type III phase-field system with a logarithmic potential. Zbl 1213.35187
Miranville, Alain; Quintanilla, Ramon
2011
A phase-field model based on a three-phase-lag heat conduction. Zbl 1213.35111
Miranville, Alain; Quintanilla, Ramon
2011
Asymptotic behavior of the Cahn-Hilliard-Oono equation. Zbl 1304.35342
Miranville, Alain
2011
Analysis of the Cahn-Hilliard equation with a chemical potential dependent mobility. Zbl 1241.35024
Grasselli, Maurizio; Miranville, Alain; Rossi, Riccarda; Schimperna, Giulio
2011
A doubly nonlinear parabolic equation with a singular potential. Zbl 1207.35067
Cherfils, Laurence; Gatti, Stefania; Miranville, Alain
2011
The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Zbl 1203.35046
Miranville, Alain; Zelik, Sergey
2010
The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials. Zbl 1194.35074
Grasselli, Maurizio; Miranville, Alain; Schimperna, Giulio
2010
Long time behavior of the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions. Zbl 1223.35067
Gilardi, Gianni; Miranville, Alain; Schimperna, Giulio
2010
Pullback exponential attractors. Zbl 1303.37032
Langa, José A.; Miranville, Alain; Real, José
2010
Continuous families of exponential attractors for singularly perturbed equations with memory. Zbl 1196.35054
Gatti, Stefania; Miranville, Alain; Pata, Vittorino; Zelik, Sergey
2010
Phase-field systems with nonlinear coupling and dynamic boundary conditions. Zbl 1184.35053
Cavaterra, Cecilia; Gal, Ciprian G.; Grasselli, Maurizio; Miranville, Alain
2010
Singularly perturbed 1D Cahn-Hilliard equation revisited. Zbl 1387.35341
Bonfoh, Ahmed; Grasselli, Maurizio; Miranville, Alain
2010
Inertial manifolds for a singular perturbation of the viscous Cahn-Hilliard-Gurtin equation. Zbl 1211.35054
Bonfoh, Ahmed; Grasselli, Maurizio; Miranville, Alain
2010
On a doubly nonlinear Cahn-Hilliard-Gurtin system. Zbl 1203.35045
Miranville, Alain; Schimperna, Giulio
2010
A Caginalp phase-field system with a nonlinear coupling. Zbl 1197.35082
Miranville, Alain; Quintanilla, Ramon
2010
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions. Zbl 1172.35417
Gilardi, Gianni; Miranville, A.; Schimperna, Giulio
2009
On the Caginalp system with dynamic boundary conditions and singular potentials. Zbl 1212.35012
Cherfils, Laurence; Miranville, Alain
2009
Some generalizations of the Caginalp phase-field system. Zbl 1178.35194
Miranville, Alain; Quintanilla, Ramon
2009
A generalization of the Caginalp phase-field system based on the Cattaneo law. Zbl 1167.35304
Miranville, Alain; Quintanilla, Ramon
2009
...and 82 more Documents
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#### Cited by 826 Authors

 100 Miranville, Alain M. 39 Grasselli, Maurizio 36 Zelik, Sergey V. 35 Colli, Pierluigi 30 Quintanilla de Latorre, Ramón 26 Gal, Ciprian Gheorghe Sorin 25 Pata, Vittorino 22 Gilardi, Gianni 22 Schimperna, Giulio 21 Conti, Monica C. 21 Gatti, Stefania 17 Rocca, Elisabetta 16 Sprekels, Jürgen 15 Cherfils, Laurence 13 Giorgini, Andrea 13 Sun, Chunyou 13 Temam, Roger Meyer 13 Wu, Hao 12 Chepyzhov, Vladimir V. 12 Scarpa, Luca 11 Zhong, Chengkui 10 Bonfoh, Ahmed S. 10 Yang, Zhijian 9 Fukao, Takeshi 9 Shomberg, Joseph L. 8 Efendiev, Messoud 8 Garcke, Harald 8 Ilyin, Alexei A. 8 Kloeden, Peter Eris 8 Lam, Kei Fong 8 Moroşanu, Costică 8 Signori, Andrea 8 Zhou, Shengfan 7 Fakih, Hussein 7 Kalantarov, Varga K. 7 Marchini, Elsa Maria 7 Pražák, Dalibor 7 Yang, Meihua 7 Zhao, Xiaopeng 6 Bonetti, Elena 6 Duan, Jinqiao 6 Lasiecka, Irena 6 Magaña, Antonio 6 Marinoschi, Gabriela 6 Pierre, Morgan 6 Rossi, Riccarda 6 Segatti, Antonio 6 Webster, Justin T. 6 Yang, Xinguang 5 Chueshov, Igor’ Dmitrievich 5 Duan, Ning 5 Fernández, Jose Ramon 5 Goubet, Olivier 5 Heinemann, Christian 5 Kraus, Christiane 5 Li, Yongjun 5 Makki, Ahmad 5 Marín-Rubio, Pedro 5 Nolasco de Carvalho, Alexandre 5 Petzeltová, Hana 5 Savostianov, Anton K. 5 Sonner, Stefanie 5 Tachim Medjo, Theodore 5 Tomassetti, Giuseppe 5 Wang, Cheng 5 Yang, Lu 5 Zhu, Peicheng 4 Abdallah, Ahmed Y. 4 Bazarra, Noelia 4 Bulíček, Miroslav 4 Caraballo Garrido, Tomás 4 Cavaterra, Cecilia 4 Chehab, Jean-Paul 4 Czaja, Radosław 4 Davoli, Elisa 4 Dell’Oro, Filippo 4 Geredeli, Pelin G. 4 Li, Yinghua 4 Ma, To Fu 4 Mammeri, Youcef 4 Meng, Fengjuan 4 Ostoja-Starzewski, Martin 4 Real Anguas, José 4 Straughan, Brian 4 Verani, Marco 4 Vishik, Marko Iosifovich 4 Wang, Xiaoming 4 Wise, Steven M. 4 Yin, Jingxue 4 Zheng, Songmu 3 Alber, Hans-Dieter 3 Aouadi, Moncef 3 Boldrini, José Luiz 3 Boukrouche, Mahdi 3 Chai, Xiaojuan 3 Cholewa, Jan W. 3 Coti Zelati, Michele 3 Cui, Hongyong 3 di Plinio, Francesco 3 Ding, Pengyan ...and 726 more Authors
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#### Cited in 184 Serials

 49 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 48 Journal of Differential Equations 47 Journal of Mathematical Analysis and Applications 33 Communications on Pure and Applied Analysis 29 Discrete and Continuous Dynamical Systems. Series B 26 Discrete and Continuous Dynamical Systems 26 Nonlinear Analysis. Real World Applications 23 Mathematical Methods in the Applied Sciences 17 Physica D 16 Applied Mathematics and Optimization 14 Applied Mathematics Letters 14 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 12 Applicable Analysis 11 Applied Mathematics and Computation 11 Discrete and Continuous Dynamical Systems. Series S 10 ZAMP. Zeitschrift für angewandte Mathematik und Physik 10 Quarterly of Applied Mathematics 10 SIAM Journal on Mathematical Analysis 10 Journal of Evolution Equations 9 Journal of Mathematical Physics 9 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Archive for Rational Mechanics and Analysis 8 Computers & Mathematics with Applications 8 Journal of Scientific Computing 8 Applications of Mathematics 8 Journal of Applied Analysis and Computation 7 Journal of Computational Physics 7 Journal of Computational and Applied Mathematics 7 Asymptotic Analysis 7 NoDEA. Nonlinear Differential Equations and Applications 7 Evolution Equations and Control Theory 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Journal of Nonlinear Science 6 Abstract and Applied Analysis 6 Boundary Value Problems 5 International Journal of Engineering Science 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Transactions of the American Mathematical Society 5 Applied Numerical Mathematics 5 Journal of Elasticity 5 Journal of Dynamics and Differential Equations 5 Central European Journal of Mathematics 5 Advances in Nonlinear Analysis 4 Acta Mechanica 4 Bulletin of the Australian Mathematical Society 4 Communications in Mathematical Physics 4 Nonlinearity 4 SIAM Journal on Control and Optimization 4 European Journal of Applied Mathematics 4 Discrete Dynamics in Nature and Society 4 Journal of Mathematical Fluid Mechanics 4 Mediterranean Journal of Mathematics 4 SIAM Journal on Imaging Sciences 4 Electronic Research Archive 3 Ricerche di Matematica 3 Stochastic Analysis and Applications 3 Numerical Algorithms 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Calculus of Variations and Partial Differential Equations 3 Russian Journal of Mathematical Physics 3 Milan Journal of Mathematics 3 Complex Variables and Elliptic Equations 3 Journal of Function Spaces 3 Journal of Elliptic and Parabolic Equations 3 AIMS Mathematics 2 Computers and Fluids 2 International Journal of Control 2 Mathematical Notes 2 Russian Mathematical Surveys 2 Mathematics of Computation 2 Chaos, Solitons and Fractals 2 Annales Polonici Mathematici 2 Journal of Functional Analysis 2 Mathematische Nachrichten 2 Meccanica 2 Numerical Functional Analysis and Optimization 2 Numerische Mathematik 2 Chinese Annals of Mathematics. Series B 2 Acta Applicandae Mathematicae 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Communications in Partial Differential Equations 2 Continuum Mechanics and Thermodynamics 2 SIAM Journal on Scientific Computing 2 Topological Methods in Nonlinear Analysis 2 Electronic Journal of Differential Equations (EJDE) 2 Computational and Applied Mathematics 2 Journal of Convex Analysis 2 Sbornik: Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Chaos 2 Acta Mathematica Sinica. English Series 2 Communications in Nonlinear Science and Numerical Simulation 2 Computational Geosciences 2 Journal of Dynamical and Control Systems 2 Qualitative Theory of Dynamical Systems 2 Dynamical Systems 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Stochastics and Dynamics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis ...and 84 more Serials
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#### Cited in 34 Fields

 703 Partial differential equations (35-XX) 182 Dynamical systems and ergodic theory (37-XX) 142 Fluid mechanics (76-XX) 121 Mechanics of deformable solids (74-XX) 92 Classical thermodynamics, heat transfer (80-XX) 83 Numerical analysis (65-XX) 49 Statistical mechanics, structure of matter (82-XX) 39 Integral equations (45-XX) 39 Calculus of variations and optimal control; optimization (49-XX) 36 Biology and other natural sciences (92-XX) 26 Ordinary differential equations (34-XX) 24 Operator theory (47-XX) 21 Probability theory and stochastic processes (60-XX) 14 Systems theory; control (93-XX) 10 Measure and integration (28-XX) 10 Information and communication theory, circuits (94-XX) 8 Computer science (68-XX) 8 Geophysics (86-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Functional analysis (46-XX) 5 Optics, electromagnetic theory (78-XX) 5 Operations research, mathematical programming (90-XX) 3 Real functions (26-XX) 3 Potential theory (31-XX) 2 General and overarching topics; collections (00-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX)