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## Mel’nyk, Taras A.

Compute Distance To:
 Author ID: melnyk.taras-a Published as: Mel’Nyk, Taras; Mel’nyk, T. A.; Mel’nyk, Taras; Mel’nyk, Taras A.; Melnyk, Taras A. External Links: MGP
 Documents Indexed: 71 Publications since 1994, including 1 Book
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#### Co-Authors

 22 single-authored 11 De Maio, Umberto 6 Chechkin, Gregory Aleksandrovich 6 Durante, Tiziana 6 Klevtsovskiy, Arsen V. 3 D’Apice, Ciro 3 Gaudiello, Antonio 3 Nakvasiuk, Iulia A. 3 Popov, Andrey V. 3 Sivak, Olena A. 2 Chechkina, Tatiana P. 2 Nazarov, Sergeĭ Aleksandrovich 2 Perugia, Carmen 2 Vashchuk, P. S. 1 Argatov, Ivan I. 1 Blanchard, Dominique 1 Kazmerchuk, Yu. A. 1 Klevtsovs’kyi, A. V. 1 Nakvasiuk, Yu. A. 1 Sadovyi, D. Yu. 1 Sadovyi, Dmytro 1 Sadovyj, Dmytro 1 Vaschuk, P. S. 1 Vasylyeva, Nataliya V. 1 Wendland, Wolfgang L.
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#### Serials

 6 Mathematical Methods in the Applied Sciences 4 Asymptotic Analysis 4 Journal of Mathematical Sciences (New York) 3 Ukraïns’kyĭ Matematychnyĭ Zhurnal 3 Neliniĭni Kolyvannya 3 Visnyk. Seriya: Fizyko-Matematychni Nauky. Kyïvs’kyĭ Universytet Imeni Tarasa Shevchenka 3 Nonlinear Oscillations 2 Applicable Analysis 2 Ricerche di Matematica 2 Zeitschrift für Analysis und ihre Anwendungen 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky 2 Nonlinear Oscillations 2 Journal of Mathematical Physics, Analysis, Geometry 1 Journal of Mathematical Analysis and Applications 1 Nonlinearity 1 Ukrainian Mathematical Journal 1 Journal of Differential Equations 1 Journal of Optimization Theory and Applications 1 Visnyk L’vivs’kogo Universytetu. Seriya Mekhaniko-Matematychna 1 SIAM Journal on Mathematical Analysis 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Russian Journal of Mathematical Physics 1 St. Petersburg Mathematical Journal 1 NoDEA. Nonlinear Differential Equations and Applications 1 Izvestiya: Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Journal of Inequalities and Applications 1 European Journal of Mechanics. A. Solids 1 Visnyk. Matematyka. Mekhanika. Kyïvs’kyĭ Universytet Imeni Tarasa Shevchenka 1 Nonlinear Boundary Value Problems 1 Networks and Heterogeneous Media 1 Matematychnyĭ Visnyk Naukovogo Tovarystva Im. Shevchenka 1 Ukraïns’kyĭ Matematychnyĭ Visnyk 1 International Journal of Biomathematics 1 Carpathian Mathematical Publications 1 Open Mathematics 1 SpringerBriefs in Mathematics
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#### Fields

 69 Partial differential equations (35-XX) 26 Mechanics of deformable solids (74-XX) 10 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Fluid mechanics (76-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 Ordinary differential equations (34-XX) 1 Numerical analysis (65-XX) 1 Classical thermodynamics, heat transfer (80-XX)

#### Citations contained in zbMATH Open

49 Publications have been cited 349 times in 122 Documents Cited by Year
Homogenization of the Poisson equation in a thick periodic junction. Zbl 0938.35021
Mel’nyk, T. A.
1999
Boundary homogenization and reduction of dimension in a Kirchhoff-Love plate. Zbl 1149.74037
Blanchard, Dominique; Gaudiello, Antonio; Mel’nyk, Taras A.
2008
Asymptotic approximation for the solution to the Robin problem in a thick multi-level junction. Zbl 1093.35011
De Maio, U.; Durante, T.; Mel’nyk, T. A.
2005
Homogenization of a boundary-value problem with a nonlinear boundary condition in a thick junction of type 3:2:1. Zbl 1145.35327
Mel’nyk, Taras A.
2008
Asymptotic structure of the spectrum of the Neumann problem in a thin comb-like domain. Zbl 0814.73017
Mel’nyk, Taras A.; Nazarov, Serguei A.
1994
Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1. Zbl 1246.49005
Durante, Tiziana; Mel’nyk, Taras A.
2012
Asymptotic analysis of a perturbed parabolic problem in a thick junction of type 3:2:2. Zbl 1127.35310
D’Apice, C.; De Maio, U.; Mel’nyk, T. A.
2007
Asymptotic analysis of a boundary-value problem in a cascade thick junction with a random transmission zone. Zbl 1180.35071
Chechkin, G. A.; Chechkina, T. P.; D’Apice, C.; de Maio, U.; Mel’nyk, T. A.
2009
Vibrations of a thick periodic junction with concentrated masses. Zbl 1013.35006
Mel’nyk, Taras A.
2001
Asymptotic analysis of an optimal control problem involving a thick two-level junction with alternate type of controls. Zbl 1185.49027
Durante, T.; Mel’nyk, T. A.
2010
Asymptotic behavior of eigenvalues and eigenfunctions of the Steklov problem in a thick periodic junction. Zbl 1053.35115
Mel’nyk, T. A.
2001
Asymptotic analysis of a spectral problem in a periodic thick junction of type 3:2:1. Zbl 0983.35044
Mel’nyk, T. A.
2000
Homogenization of the Signorini boundary-value problem in a thick junction and boundary integral equations for the homogenized problem. Zbl 1217.35019
Mel’nyk, T. A.; Nakvasiuk, Iu. A.; Wendland, W. L.
2011
Asymptotic analysis of boundary-value problems in thin perforated domains with rapidly varying thickness. Zbl 1334.74057
Mel’nyk, T. A.; Popov, A. V.
2010
Asymptotic approximation for the solution to a semi-linear parabolic problem in a thick junction with the branched structure. Zbl 06383571
Mel’nyk, Taras A.
2015
Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary. Zbl 1403.35035
Gaudiello, Antonio; Mel’nyk, Taras
2018
Homogenization of 3D thick cascade junction with a random transmission zone periodic in one direction. Zbl 1196.35035
Chechkin, G. A.; Chechkina, T. P.; D’Apice, C.; de Maio, U.; Mel’nyk, T. A.
2010
Homogenization of a singularly perturbed parabolic problem in a thick periodic junction of the type 3:2:1. Zbl 0987.35019
Mel’nyk, T. A.
2000
Asymptotics of eigenelements to spectral problem in thick cascade junction with concentrated masses. Zbl 1254.35168
Chechkin, Gregory A.; Mel’nyk, Taras A.
2012
Asymptotic analysis of a boundary-value problem with nonlinear multiphase boundary interactions in a perforated domain. Zbl 1224.35107
Mel’nyk, T. A.; Sivak, O. A.
2009
Homogenization of the Signorini boundary-value problem in a thick plane junction. Zbl 1277.35035
Kazmerchuk, Yu. A.; Mel’nyk, T. A.
2009
Asymptotic analysis of a parabolic problem in a thick two-level junction. Zbl 1144.35331
Durante, T.; Mel’nyk, T. A.
2007
Asymptotic behaviour of eigenvalues and eigenfunctions of the Fourier problem in a thick multilevel junction. Zbl 1118.35018
Mel’nyk, T. A.
2006
Homogenization of the Robin problem for the Poisson equation in a thick multi-structure of type 3:2:2. Zbl 1071.35014
De Maio, U.; Mel’nyk, T. A.
2005
Asymptotic expansion for the solution to a boundary-value problem in a thin cascade domain with a local joint. Zbl 1348.35019
Klevtsovskiy, A. V.; Mel’nyk, T. A.
2016
Spatial-skin effect for eigenvibrations of a thick cascade junction with ’heavy’ concentrated masses. Zbl 1282.35037
Chechkin, G. A.; Mel’nyk, T. A.
2014
Asymptotic analysis of boundary-value problems in thick cascade junctions. Zbl 1164.35316
Mel’nyk, T. A.; Chechkin, G. A.
2008
Homogenization of the Neumann-Fourier problem in a thick two-level junction of type 3:2:1. Zbl 1141.35328
Mel’nyk, T. A.; Vashchuk, P. S.
2006
Homogenization of the Neumann problem in thick multi-structures of type 3 : 2 : 2. Zbl 1072.35029
De Maio, U.; Mel’nyk, T. A.
2005
Asymptotic approximations of the solution to a boundary value problem in a thin aneurysm type domain. Zbl 1458.35144
Klevtsovskiy, A. V.; Mel’nyk, T. A.
2017
Homogenization of a semilinear variational inequality in a thick multi-level junction. Zbl 1333.35004
Mel’nyk, Taras A.; Nakvasiuk, Iulia A.
2016
Homogenization of a contact problem for a system of densely situated punches. Zbl 0996.74061
Argatov, Ivan I.; Mel’nyk, Taras A.
2001
On free vibrations of a thick periodic junction with concentrated masses on the fine rods. Zbl 0953.35016
Mel’nyk, T. A.
1999
Asymptotic analysis of a mathematical model of the atherosclerosis development. Zbl 1409.92073
Mel’Nyk, Taras
2019
Asymptotic approximations for solutions to quasilinear and linear elliptic problems with different perturbed boundary conditions in perforated domains. Zbl 1233.35018
Mel’nyk, Taras A.; Sivak, Olena A.
2011
Averaging of a boundary-value problem with variation of the type of boundary conditions in a thick two-level junction. Zbl 1150.35360
Mel’nyk, T. A.; Vaschuk, P. S.
2005
Averaging of the Robin problem for a thick multilevel junction. Zbl 1150.35358
De Maio, U.; Mel’nyk, T. A.; Perugia, C.
2004
Hausdorff convergence and asymptotic estimates of the spectrum of a perturbed operator. Zbl 1016.47014
Mel’nyk, T. A.
2001
Vibrations and pseudovibrations of thick periodic junctions with concentrated masses. Zbl 0984.35119
Mel’nyk, T. A.
2001
Asymptotic analysis of the Neumann problem on the junction of a body and thin heavy rods. Zbl 0988.74043
Mel’nyk, T. A.; Nazarov, S. A.
2000
Homogenization of a nonlinear monotone problem with a big nonlinear Signorini boundary interaction in a domain with highly rough boundary. Zbl 1425.35006
Gaudiello, Antonio; Mel’nyk, Taras
2019
Asymptotic approximation for the solution to a semilinear parabolic problem in a thin star-shaped junction. Zbl 1380.35150
Klevtsovskiy, Arsen; Mel’nyk, Taras
2018
Eigenvibrations of thick cascade junctions with ‘very heavy’ concentrated masses. Zbl 1332.35028
Mel’nyk, T. A.; Chechkin, G. A.
2015
Homogenization of a parabolic Signorini boundary value problem in a thick plane junction. Zbl 1348.35022
Mel’nyk, T. A.; Nakvasiuk, Iu. A.
2012
Homogenization of a quasilinear parabolic problem with different alternating nonlinear Fourier boundary conditions in a two-level thick junction of the type 3:2:2. Zbl 1259.35026
Mel’nyk, T. A.; Sadovyi, D. Yu.
2012
Asymptotic expansion for the solution of an elliptic problem with boundary multi-phase interactions of the Dirichlet and Neumann types in a perforated domain. Zbl 1224.35022
Mel’nyk, T. A.; Sivak, O. A.
2010
Asymptotic approximation for the solution of a boundary-value problem with varying type of boundary conditions in a thick two-level junction. Zbl 1262.35177
Durante, T.; Mel’nyk, T. A.; Vashchuk, P. S.
2006
Asymptotic analysis of the Neumann problem for the Ukawa equation in a thick multi-structure of type 3:2:2. Zbl 1160.35327
De Maio, U.; Mel’nyk, T. A.
2005
Asymptotic behaviour of eigenvalues and eigenfunctions for the Fourier problem in a thick junction of the type 3:2:1. Zbl 1071.35534
Mel’nyk, T. A.
2001
Asymptotic analysis of a mathematical model of the atherosclerosis development. Zbl 1409.92073
Mel’Nyk, Taras
2019
Homogenization of a nonlinear monotone problem with a big nonlinear Signorini boundary interaction in a domain with highly rough boundary. Zbl 1425.35006
Gaudiello, Antonio; Mel’nyk, Taras
2019
Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary. Zbl 1403.35035
Gaudiello, Antonio; Mel’nyk, Taras
2018
Asymptotic approximation for the solution to a semilinear parabolic problem in a thin star-shaped junction. Zbl 1380.35150
Klevtsovskiy, Arsen; Mel’nyk, Taras
2018
Asymptotic approximations of the solution to a boundary value problem in a thin aneurysm type domain. Zbl 1458.35144
Klevtsovskiy, A. V.; Mel’nyk, T. A.
2017
Asymptotic expansion for the solution to a boundary-value problem in a thin cascade domain with a local joint. Zbl 1348.35019
Klevtsovskiy, A. V.; Mel’nyk, T. A.
2016
Homogenization of a semilinear variational inequality in a thick multi-level junction. Zbl 1333.35004
Mel’nyk, Taras A.; Nakvasiuk, Iulia A.
2016
Asymptotic approximation for the solution to a semi-linear parabolic problem in a thick junction with the branched structure. Zbl 06383571
Mel’nyk, Taras A.
2015
Eigenvibrations of thick cascade junctions with ‘very heavy’ concentrated masses. Zbl 1332.35028
Mel’nyk, T. A.; Chechkin, G. A.
2015
Spatial-skin effect for eigenvibrations of a thick cascade junction with ’heavy’ concentrated masses. Zbl 1282.35037
Chechkin, G. A.; Mel’nyk, T. A.
2014
Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1. Zbl 1246.49005
Durante, Tiziana; Mel’nyk, Taras A.
2012
Asymptotics of eigenelements to spectral problem in thick cascade junction with concentrated masses. Zbl 1254.35168
Chechkin, Gregory A.; Mel’nyk, Taras A.
2012
Homogenization of a parabolic Signorini boundary value problem in a thick plane junction. Zbl 1348.35022
Mel’nyk, T. A.; Nakvasiuk, Iu. A.
2012
Homogenization of a quasilinear parabolic problem with different alternating nonlinear Fourier boundary conditions in a two-level thick junction of the type 3:2:2. Zbl 1259.35026
Mel’nyk, T. A.; Sadovyi, D. Yu.
2012
Homogenization of the Signorini boundary-value problem in a thick junction and boundary integral equations for the homogenized problem. Zbl 1217.35019
Mel’nyk, T. A.; Nakvasiuk, Iu. A.; Wendland, W. L.
2011
Asymptotic approximations for solutions to quasilinear and linear elliptic problems with different perturbed boundary conditions in perforated domains. Zbl 1233.35018
Mel’nyk, Taras A.; Sivak, Olena A.
2011
Asymptotic analysis of an optimal control problem involving a thick two-level junction with alternate type of controls. Zbl 1185.49027
Durante, T.; Mel’nyk, T. A.
2010
Asymptotic analysis of boundary-value problems in thin perforated domains with rapidly varying thickness. Zbl 1334.74057
Mel’nyk, T. A.; Popov, A. V.
2010
Homogenization of 3D thick cascade junction with a random transmission zone periodic in one direction. Zbl 1196.35035
Chechkin, G. A.; Chechkina, T. P.; D’Apice, C.; de Maio, U.; Mel’nyk, T. A.
2010
Asymptotic expansion for the solution of an elliptic problem with boundary multi-phase interactions of the Dirichlet and Neumann types in a perforated domain. Zbl 1224.35022
Mel’nyk, T. A.; Sivak, O. A.
2010
Asymptotic analysis of a boundary-value problem in a cascade thick junction with a random transmission zone. Zbl 1180.35071
Chechkin, G. A.; Chechkina, T. P.; D’Apice, C.; de Maio, U.; Mel’nyk, T. A.
2009
Asymptotic analysis of a boundary-value problem with nonlinear multiphase boundary interactions in a perforated domain. Zbl 1224.35107
Mel’nyk, T. A.; Sivak, O. A.
2009
Homogenization of the Signorini boundary-value problem in a thick plane junction. Zbl 1277.35035
Kazmerchuk, Yu. A.; Mel’nyk, T. A.
2009
Boundary homogenization and reduction of dimension in a Kirchhoff-Love plate. Zbl 1149.74037
Blanchard, Dominique; Gaudiello, Antonio; Mel’nyk, Taras A.
2008
Homogenization of a boundary-value problem with a nonlinear boundary condition in a thick junction of type 3:2:1. Zbl 1145.35327
Mel’nyk, Taras A.
2008
Asymptotic analysis of boundary-value problems in thick cascade junctions. Zbl 1164.35316
Mel’nyk, T. A.; Chechkin, G. A.
2008
Asymptotic analysis of a perturbed parabolic problem in a thick junction of type 3:2:2. Zbl 1127.35310
D’Apice, C.; De Maio, U.; Mel’nyk, T. A.
2007
Asymptotic analysis of a parabolic problem in a thick two-level junction. Zbl 1144.35331
Durante, T.; Mel’nyk, T. A.
2007
Asymptotic behaviour of eigenvalues and eigenfunctions of the Fourier problem in a thick multilevel junction. Zbl 1118.35018
Mel’nyk, T. A.
2006
Homogenization of the Neumann-Fourier problem in a thick two-level junction of type 3:2:1. Zbl 1141.35328
Mel’nyk, T. A.; Vashchuk, P. S.
2006
Asymptotic approximation for the solution of a boundary-value problem with varying type of boundary conditions in a thick two-level junction. Zbl 1262.35177
Durante, T.; Mel’nyk, T. A.; Vashchuk, P. S.
2006
Asymptotic approximation for the solution to the Robin problem in a thick multi-level junction. Zbl 1093.35011
De Maio, U.; Durante, T.; Mel’nyk, T. A.
2005
Homogenization of the Robin problem for the Poisson equation in a thick multi-structure of type 3:2:2. Zbl 1071.35014
De Maio, U.; Mel’nyk, T. A.
2005
Homogenization of the Neumann problem in thick multi-structures of type 3 : 2 : 2. Zbl 1072.35029
De Maio, U.; Mel’nyk, T. A.
2005
Averaging of a boundary-value problem with variation of the type of boundary conditions in a thick two-level junction. Zbl 1150.35360
Mel’nyk, T. A.; Vaschuk, P. S.
2005
Asymptotic analysis of the Neumann problem for the Ukawa equation in a thick multi-structure of type 3:2:2. Zbl 1160.35327
De Maio, U.; Mel’nyk, T. A.
2005
Averaging of the Robin problem for a thick multilevel junction. Zbl 1150.35358
De Maio, U.; Mel’nyk, T. A.; Perugia, C.
2004
Vibrations of a thick periodic junction with concentrated masses. Zbl 1013.35006
Mel’nyk, Taras A.
2001
Asymptotic behavior of eigenvalues and eigenfunctions of the Steklov problem in a thick periodic junction. Zbl 1053.35115
Mel’nyk, T. A.
2001
Homogenization of a contact problem for a system of densely situated punches. Zbl 0996.74061
Argatov, Ivan I.; Mel’nyk, Taras A.
2001
Hausdorff convergence and asymptotic estimates of the spectrum of a perturbed operator. Zbl 1016.47014
Mel’nyk, T. A.
2001
Vibrations and pseudovibrations of thick periodic junctions with concentrated masses. Zbl 0984.35119
Mel’nyk, T. A.
2001
Asymptotic behaviour of eigenvalues and eigenfunctions for the Fourier problem in a thick junction of the type 3:2:1. Zbl 1071.35534
Mel’nyk, T. A.
2001
Asymptotic analysis of a spectral problem in a periodic thick junction of type 3:2:1. Zbl 0983.35044
Mel’nyk, T. A.
2000
Homogenization of a singularly perturbed parabolic problem in a thick periodic junction of the type 3:2:1. Zbl 0987.35019
Mel’nyk, T. A.
2000
Asymptotic analysis of the Neumann problem on the junction of a body and thin heavy rods. Zbl 0988.74043
Mel’nyk, T. A.; Nazarov, S. A.
2000
Homogenization of the Poisson equation in a thick periodic junction. Zbl 0938.35021
Mel’nyk, T. A.
1999
On free vibrations of a thick periodic junction with concentrated masses on the fine rods. Zbl 0953.35016
Mel’nyk, T. A.
1999
Asymptotic structure of the spectrum of the Neumann problem in a thin comb-like domain. Zbl 0814.73017
Mel’nyk, Taras A.; Nazarov, Serguei A.
1994
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#### Cited in 56 Serials

 15 Journal of Mathematical Sciences (New York) 8 Mathematical Methods in the Applied Sciences 6 Applicable Analysis 6 Journal of Mathematical Analysis and Applications 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Ukrainian Mathematical Journal 4 Communications in Contemporary Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Journal of Differential Equations 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Mathematical Analysis 3 Nonlinear Analysis. Real World Applications 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Applied Mathematics and Computation 2 Journal of Computational and Applied Mathematics 2 Ricerche di Matematica 2 Zeitschrift für Analysis und ihre Anwendungen 2 Asymptotic Analysis 2 Calculus of Variations and Partial Differential Equations 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Differential Equations 2 Communications on Pure and Applied Analysis 2 Boundary Value Problems 2 Nonlinear Oscillations 2 Evolution Equations and Control Theory 1 Archive for Rational Mechanics and Analysis 1 International Journal of Engineering Science 1 Journal of Applied Mathematics and Mechanics 1 Journal of Mathematical Biology 1 Mathematical Notes 1 Nonlinearity 1 Chaos, Solitons and Fractals 1 Prikladnaya Matematika i Mekhanika 1 Applied Mathematics and Optimization 1 Journal of Optimization Theory and Applications 1 Transactions of the Moscow Mathematical Society 1 Applied Numerical Mathematics 1 Applications of Mathematics 1 Journal of Elasticity 1 SIAM Journal on Applied Mathematics 1 Stochastic Processes and their Applications 1 Russian Journal of Mathematical Physics 1 St. Petersburg Mathematical Journal 1 NoDEA. Nonlinear Differential Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 Doklady Mathematics 1 Journal of Inequalities and Applications 1 Revista Matemática Complutense 1 Discrete and Continuous Dynamical Systems. Series B 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Analysis and Applications (Singapore) 1 Complex Variables and Elliptic Equations 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Networks and Heterogeneous Media 1 Advances in Nonlinear Analysis 1 Open Mathematics
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#### Cited in 15 Fields

 110 Partial differential equations (35-XX) 33 Mechanics of deformable solids (74-XX) 12 Operator theory (47-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 11 Fluid mechanics (76-XX) 7 Numerical analysis (65-XX) 6 Systems theory; control (93-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Measure and integration (28-XX) 2 Biology and other natural sciences (92-XX) 1 Potential theory (31-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX)