Coclite, Giuseppe Maria; di Ruvo, Lorenzo \(H^1\) solutions for a Kuramoto-Sinelshchikov-Cahn-Hilliard type equation. (English) Zbl 1514.35112 Ric. Mat. 72, No. 1, 159-180 (2023). MSC: 35G25 35K55 PDFBibTeX XMLCite \textit{G. M. Coclite} and \textit{L. di Ruvo}, Ric. Mat. 72, No. 1, 159--180 (2023; Zbl 1514.35112) Full Text: DOI
Li, Zhenbang The existence of non-blow-up phenomenon for a generalized nonlocal Cahn-Hilliard equation with degenerate mobility. (English) Zbl 1512.35085 Boll. Unione Mat. Ital. 16, No. 1, 65-79 (2023). MSC: 35B40 35B44 35K35 35K59 35K65 PDFBibTeX XMLCite \textit{Z. Li}, Boll. Unione Mat. Ital. 16, No. 1, 65--79 (2023; Zbl 1512.35085) Full Text: DOI
Coclite, Giuseppe Maria; di Ruvo, Lorenzo On a diffusion model for growth and dispersal in a population. (English) Zbl 1512.35159 Commun. Pure Appl. Anal. 22, No. 4, 1194-1225 (2023). MSC: 35G25 35K58 PDFBibTeX XMLCite \textit{G. M. Coclite} and \textit{L. di Ruvo}, Commun. Pure Appl. Anal. 22, No. 4, 1194--1225 (2023; Zbl 1512.35159) Full Text: DOI
Wang, Ruijing; Li, Chunqiu The convergence of attractors for some discrete Cahn-Hilliard systems. (English) Zbl 1505.35048 Discrete Dyn. Nat. Soc. 2022, Article ID 8758294, 7 p. (2022). MSC: 35B40 35K60 35K55 65M60 PDFBibTeX XMLCite \textit{R. Wang} and \textit{C. Li}, Discrete Dyn. Nat. Soc. 2022, Article ID 8758294, 7 p. (2022; Zbl 1505.35048) Full Text: DOI
Fusco, Giorgio Periodic motions for multi-wells potentials and layers dynamic for the vector Allen-Cahn equation. (English) Zbl 1509.35135 J. Dyn. Differ. Equations 34, No. 4, 3165-3215 (2022). MSC: 35K58 35B10 35B25 PDFBibTeX XMLCite \textit{G. Fusco}, J. Dyn. Differ. Equations 34, No. 4, 3165--3215 (2022; Zbl 1509.35135) Full Text: DOI arXiv
Folino, Raffaele; Ríos, Luis F. López; Strani, Marta On a generalized Cahn-Hilliard model with \(p\)-Laplacian. (English) Zbl 1494.35034 Adv. Differ. Equ. 27, No. 9-10, 647-682 (2022). MSC: 35B40 35B25 35B36 35K35 35K92 82C26 PDFBibTeX XMLCite \textit{R. Folino} et al., Adv. Differ. Equ. 27, No. 9--10, 647--682 (2022; Zbl 1494.35034) Full Text: arXiv Link
Biesenbach, Sarah; Schubert, Richard; Westdickenberg, Maria G. Optimal relaxation of bump-like solutions of the one-dimensional Cahn-Hilliard equation. (English) Zbl 1491.35031 Commun. Partial Differ. Equations 47, No. 3, 489-548 (2022); erratum ibid. 48, No. 5, 792-793 (2023). Reviewer: Gabriela Marinoschi (Bucureşti) MSC: 35B40 35K35 35K58 PDFBibTeX XMLCite \textit{S. Biesenbach} et al., Commun. Partial Differ. Equations 47, No. 3, 489--548 (2022; Zbl 1491.35031) Full Text: DOI arXiv
Li, Bing; Wang, Fang; Xue, Ling; Yang, Kai; Zhao, Kun On the Cahn-Hilliard-Brinkman equations in \(\mathbb{R}^4\): global well-posedness. (English) Zbl 1499.35505 Ann. Appl. Math. 37, No. 4, 513-536 (2021). MSC: 35Q35 35A01 35A02 35A09 35G25 PDFBibTeX XMLCite \textit{B. Li} et al., Ann. Appl. Math. 37, No. 4, 513--536 (2021; Zbl 1499.35505) Full Text: DOI
Westdickenberg, Maria G. On the metastability of the \(1-d\) Allen-Cahn equation. (English) Zbl 1478.35042 J. Dyn. Differ. Equations 33, No. 4, 1853-1879 (2021). MSC: 35B40 35K58 35K30 PDFBibTeX XMLCite \textit{M. G. Westdickenberg}, J. Dyn. Differ. Equations 33, No. 4, 1853--1879 (2021; Zbl 1478.35042) Full Text: DOI
Antonopoulou, D. C.; Karali, G.; Tzirakis, K. Layer dynamics for the one dimensional \(\varepsilon\)-dependent Cahn-Hilliard/Allen-Cahn equation. (English) Zbl 1472.35024 Calc. Var. Partial Differ. Equ. 60, No. 6, Paper No. 207, 58 p. (2021). MSC: 35B25 35B40 35K35 35K58 PDFBibTeX XMLCite \textit{D. C. Antonopoulou} et al., Calc. Var. Partial Differ. Equ. 60, No. 6, Paper No. 207, 58 p. (2021; Zbl 1472.35024) Full Text: DOI arXiv
Kulikov, A. N.; Kulikov, D. A. Cahn-Hilliard equation with two spatial variables. Pattern formation. (English. Russian original) Zbl 1471.35026 Theor. Math. Phys. 207, No. 3, 782-798 (2021); translation from Teor. Mat. Fiz. 207, No. 3, 438-457 (2021). MSC: 35B32 35K35 35K58 37L10 PDFBibTeX XMLCite \textit{A. N. Kulikov} and \textit{D. A. Kulikov}, Theor. Math. Phys. 207, No. 3, 782--798 (2021; Zbl 1471.35026); translation from Teor. Mat. Fiz. 207, No. 3, 438--457 (2021) Full Text: DOI
Coclite, Giuseppe Maria; di Ruvo, Lorenzo Well-posedness of the classical solution for the Kuramto-Sivashinsky equation with anisotropy effects. (English) Zbl 1464.35144 Z. Angew. Math. Phys. 72, No. 2, Paper No. 68, 38 p. (2021). MSC: 35K30 35K58 PDFBibTeX XMLCite \textit{G. M. Coclite} and \textit{L. di Ruvo}, Z. Angew. Math. Phys. 72, No. 2, Paper No. 68, 38 p. (2021; Zbl 1464.35144) Full Text: DOI
Strani, Marta A note on the slow convergence of solutions to conservation laws with mean curvature diffusions. (English) Zbl 1460.35042 Complex Var. Elliptic Equ. 66, No. 1, 53-70 (2021). MSC: 35B40 35B35 35B25 35K20 35K93 35B36 35L02 PDFBibTeX XMLCite \textit{M. Strani}, Complex Var. Elliptic Equ. 66, No. 1, 53--70 (2021; Zbl 1460.35042) Full Text: DOI
Folino, Raffaele; Lattanzio, Corrado; Mascia, Corrado Metastability and layer dynamics for the hyperbolic relaxation of the Cahn-Hilliard equation. (English) Zbl 1458.35047 J. Dyn. Differ. Equations 33, No. 1, 75-110 (2021). MSC: 35B35 35L35 35L76 PDFBibTeX XMLCite \textit{R. Folino} et al., J. Dyn. Differ. Equations 33, No. 1, 75--110 (2021; Zbl 1458.35047) Full Text: DOI arXiv
Buttà, Paolo; Cirillo, Emilio N. M.; Sciarra, Giulio Stability of the stationary solutions of the Allen-Cahn equation with non-constant stiffness. (English) Zbl 1466.76020 Wave Motion 98, Article ID 102641, 11 p. (2020). MSC: 76E17 76E30 74N20 74H55 PDFBibTeX XMLCite \textit{P. Buttà} et al., Wave Motion 98, Article ID 102641, 11 p. (2020; Zbl 1466.76020) Full Text: DOI arXiv
Folino, Raffaele; Garrione, Maurizio; Strani, Marta Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator. (English) Zbl 1448.35310 J. Evol. Equ. 20, No. 2, 517-551 (2020). MSC: 35K59 35B25 35B35 35B36 35K20 35K93 35B40 35P15 PDFBibTeX XMLCite \textit{R. Folino} et al., J. Evol. Equ. 20, No. 2, 517--551 (2020; Zbl 1448.35310) Full Text: DOI arXiv
Folino, Raffaele; Strani, Marta On the speed rate of convergence of solutions to conservation laws with nonlinear diffusions. (English) Zbl 1445.35221 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 196, Article ID 111762, 34 p. (2020). MSC: 35K59 35B25 35B35 35B36 35B40 35L65 35P15 35K20 PDFBibTeX XMLCite \textit{R. Folino} and \textit{M. Strani}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 196, Article ID 111762, 34 p. (2020; Zbl 1445.35221) Full Text: DOI arXiv
Li, Zhenbang The existence of weak solutions for a nonlocal Cahn-Hilliard equation with degenerate mobility. (English) Zbl 1427.35143 Indian J. Pure Appl. Math. 50, No. 2, 511-529 (2019). MSC: 35K65 35Q35 35D30 35B40 PDFBibTeX XMLCite \textit{Z. Li}, Indian J. Pure Appl. Math. 50, No. 2, 511--529 (2019; Zbl 1427.35143) Full Text: DOI
Folino, Raffaele Slow motion for one-dimensional nonlinear damped hyperbolic Allen-Cahn systems. (English) Zbl 1426.35148 Electron. J. Differ. Equ. 2019, Paper No. 113, 21 p. (2019). MSC: 35L53 35B25 35K57 35L71 PDFBibTeX XMLCite \textit{R. Folino}, Electron. J. Differ. Equ. 2019, Paper No. 113, 21 p. (2019; Zbl 1426.35148) Full Text: arXiv Link
Scholtes, Sebastian; Westdickenberg, Maria G. Metastability of the Cahn-Hilliard equation in one space dimension. (English) Zbl 1513.35329 J. Differ. Equations 265, No. 4, 1528-1575 (2018); corrigendum ibid. 362, 576-580 (2023). MSC: 35K59 PDFBibTeX XMLCite \textit{S. Scholtes} and \textit{M. G. Westdickenberg}, J. Differ. Equations 265, No. 4, 1528--1575 (2018; Zbl 1513.35329) Full Text: DOI arXiv
He, Qiaolin; Liu, Chang; Shi, Xiaoding Numerical study of phase transition in van der Waals fluid. (English) Zbl 1404.76263 Discrete Contin. Dyn. Syst., Ser. B 23, No. 10, 4519-4540 (2018). MSC: 76T10 76M20 35L65 65M06 65D30 PDFBibTeX XMLCite \textit{Q. He} et al., Discrete Contin. Dyn. Syst., Ser. B 23, No. 10, 4519--4540 (2018; Zbl 1404.76263) Full Text: DOI
Bates, Peter; Fusco, Giorgio; Karali, Georgia Gradient dynamics: motion near a manifold of quasi-equilibria. (English) Zbl 1409.37076 SIAM J. Appl. Dyn. Syst. 17, No. 3, 2106-2145 (2018). Reviewer: Ahmed Youssfi (Fès) MSC: 37L25 35A15 35K58 35B40 PDFBibTeX XMLCite \textit{P. Bates} et al., SIAM J. Appl. Dyn. Syst. 17, No. 3, 2106--2145 (2018; Zbl 1409.37076) Full Text: DOI
Strani, Marta Semigroup estimates and fast-slow dynamics in parabolic-hyperbolic systems. (English) Zbl 1383.35036 Adv. Nonlinear Anal. 7, No. 1, 117-138 (2018). MSC: 35B45 35B36 35B40 35P10 47A10 47D06 PDFBibTeX XMLCite \textit{M. Strani}, Adv. Nonlinear Anal. 7, No. 1, 117--138 (2018; Zbl 1383.35036) Full Text: DOI
Cheng, Kelong; Feng, Wenqiang Global well-posedness of strong solution for the three dimensional dynamic Cahn-Hilliard-Stokes model. (English) Zbl 1412.35170 J. Nonlinear Sci. Appl. 10, No. 8, 4209-4221 (2017). MSC: 35K55 76D05 PDFBibTeX XMLCite \textit{K. Cheng} and \textit{W. Feng}, J. Nonlinear Sci. Appl. 10, No. 8, 4209--4221 (2017; Zbl 1412.35170) Full Text: DOI
Folino, Raffaele; Lattanzio, Corrado; Mascia, Corrado; Strani, Marta Metastability for nonlinear convection-diffusion equations. (English) Zbl 1373.35157 NoDEA, Nonlinear Differ. Equ. Appl. 24, No. 4, Paper No. 35, 20 p. (2017). MSC: 35K20 35B25 35B40 PDFBibTeX XMLCite \textit{R. Folino} et al., NoDEA, Nonlinear Differ. Equ. Appl. 24, No. 4, Paper No. 35, 20 p. (2017; Zbl 1373.35157) Full Text: DOI
Drábek, Pavel; Robinson, Stephen B. Convergence to higher-energy stationary solutions of a bistable equation with non-smooth reaction term. (English) Zbl 1386.35175 Z. Angew. Math. Phys. 68, No. 3, Paper No. 67, 19 p. (2017). MSC: 35K55 35B41 35B40 35K58 PDFBibTeX XMLCite \textit{P. Drábek} and \textit{S. B. Robinson}, Z. Angew. Math. Phys. 68, No. 3, Paper No. 67, 19 p. (2017; Zbl 1386.35175) Full Text: DOI
Kuto, Kousuke; Mori, Tatsuki; Tsujikawa, Tohru; Yotsutani, Shoji Secondary bifurcation for a nonlocal Allen-Cahn equation. (English) Zbl 1382.34025 J. Differ. Equations 263, No. 5, 2687-2714 (2017). Reviewer: Tatuana Badokina (Saransk) MSC: 34B08 34C23 34B10 34B09 PDFBibTeX XMLCite \textit{K. Kuto} et al., J. Differ. Equations 263, No. 5, 2687--2714 (2017; Zbl 1382.34025) Full Text: DOI
Folino, Raffaele Slow motion for a hyperbolic variation of Allen-Cahn equation in one space dimension. (English) Zbl 1391.35028 J. Hyperbolic Differ. Equ. 14, No. 1, 1-26 (2017). Reviewer: Christos Sourdis (Torino) MSC: 35B25 35K57 35L20 35L71 PDFBibTeX XMLCite \textit{R. Folino}, J. Hyperbolic Differ. Equ. 14, No. 1, 1--26 (2017; Zbl 1391.35028) Full Text: DOI arXiv
Bates, Peter W.; Fusco, Giorgio; Jin, Jiayin Invariant manifolds of interior multi-spike states for the Cahn-Hilliard equation in higher space dimensions. (English) Zbl 1372.35019 Trans. Am. Math. Soc. 369, No. 6, 3937-3975 (2017). Reviewer: Guido Schneider (Stuttgart) MSC: 35B25 35K55 37D10 37L25 PDFBibTeX XMLCite \textit{P. W. Bates} et al., Trans. Am. Math. Soc. 369, No. 6, 3937--3975 (2017; Zbl 1372.35019) Full Text: DOI
Qin, Cong; Lai, Xin; Hao, Jianghao; Chen, Xinfu; Zhang, Yajing Dynamics of spike in a Keller-Segel’s minimal chemotaxis model. (English) Zbl 1364.35128 Discrete Contin. Dyn. Syst. 37, No. 2, 1109-1127 (2017). MSC: 35K51 35B40 92C17 92D15 PDFBibTeX XMLCite \textit{C. Qin} et al., Discrete Contin. Dyn. Syst. 37, No. 2, 1109--1127 (2017; Zbl 1364.35128) Full Text: DOI
Strani, Marta Long time dynamics of layered solutions to the shallow water equations. (English) Zbl 1358.35132 Bull. Braz. Math. Soc. (N.S.) 47, No. 2, 765-777 (2016). MSC: 35Q35 76D03 76D05 35B65 35L04 35B40 PDFBibTeX XMLCite \textit{M. Strani}, Bull. Braz. Math. Soc. (N.S.) 47, No. 2, 765--777 (2016; Zbl 1358.35132) Full Text: DOI
Luo, Zhendong; Teng, Fei An effective finite element Newton method for 2D \(p\)-Laplace equation with particular initial iterative function. (English) Zbl 1349.65629 J. Inequal. Appl. 2016, Paper No. 281, 24 p. (2016). MSC: 65N30 65N15 35J25 PDFBibTeX XMLCite \textit{Z. Luo} and \textit{F. Teng}, J. Inequal. Appl. 2016, Paper No. 281, 24 p. (2016; Zbl 1349.65629) Full Text: DOI
Strani, Marta Slow dynamics in reaction-diffusion systems. (English) Zbl 1342.35152 Asymptotic Anal. 98, No. 1-2, 131-154 (2016). MSC: 35K57 35B40 35K20 PDFBibTeX XMLCite \textit{M. Strani}, Asymptotic Anal. 98, No. 1--2, 131--154 (2016; Zbl 1342.35152) Full Text: DOI arXiv
Hillen, T.; Greese, B.; Martin, J.; de Vries, G. Birth-jump processes and application to forest fire spotting. (English) Zbl 1448.92374 J. Biol. Dyn. 9, Suppl. 1, 104-127 (2015). MSC: 92D40 45K05 60G50 35K57 35C07 PDFBibTeX XMLCite \textit{T. Hillen} et al., J. Biol. Dyn. 9, 104--127 (2015; Zbl 1448.92374) Full Text: DOI
Strani, Marta Metastable dynamics of internal interfaces for a convection-reaction-diffusion equation. (English) Zbl 1439.35212 Nonlinearity 28, No. 12, 4331-4368 (2015). MSC: 35K20 35B36 35B40 35P15 PDFBibTeX XMLCite \textit{M. Strani}, Nonlinearity 28, No. 12, 4331--4368 (2015; Zbl 1439.35212) Full Text: DOI arXiv
Bertini, Lorenzo; Brassesco, Stella; Buttà, Paolo Front fluctuations for the stochastic Cahn-Hilliard equation. (English) Zbl 1318.82033 Braz. J. Probab. Stat. 29, No. 2, 336-371 (2015). MSC: 82C31 35Q35 35R60 82B24 PDFBibTeX XMLCite \textit{L. Bertini} et al., Braz. J. Probab. Stat. 29, No. 2, 336--371 (2015; Zbl 1318.82033) Full Text: DOI arXiv Euclid
Strani, Marta Slow motion of internal shock layers for the Jin-Xin system in one space dimension. (English) Zbl 1316.35015 J. Dyn. Differ. Equations 27, No. 1, 1-27 (2015). MSC: 35B25 35L50 35L67 PDFBibTeX XMLCite \textit{M. Strani}, J. Dyn. Differ. Equations 27, No. 1, 1--27 (2015; Zbl 1316.35015) Full Text: DOI arXiv
Mascia, Corrado; Strani, Marta Metastability for scalar conservation laws in a bounded domain. (English) Zbl 1331.35225 ESAIM, Proc. Surv. 45, 247-254 (2014). MSC: 35L65 35L50 PDFBibTeX XMLCite \textit{C. Mascia} and \textit{M. Strani}, ESAIM, Proc. Surv. 45, 247--254 (2014; Zbl 1331.35225) Full Text: DOI
Bates, Peter W.; Jin, Jiayin Global dynamics of boundary droplets. (English) Zbl 1315.37049 Discrete Contin. Dyn. Syst. 34, No. 1, 1-17 (2014). Reviewer: Matheus Cheque Bortolan (Lima) MSC: 37L25 37D10 35B25 35K57 35B42 PDFBibTeX XMLCite \textit{P. W. Bates} and \textit{J. Jin}, Discrete Contin. Dyn. Syst. 34, No. 1, 1--17 (2014; Zbl 1315.37049) Full Text: DOI
Lowengrub, John; Titi, Edriss; Zhao, Kun Analysis of a mixture model of tumor growth. (English) Zbl 1292.35153 Eur. J. Appl. Math. 24, No. 5, 691-734 (2013). MSC: 35K59 35K35 92C37 35Q92 35D35 35B40 PDFBibTeX XMLCite \textit{J. Lowengrub} et al., Eur. J. Appl. Math. 24, No. 5, 691--734 (2013; Zbl 1292.35153) Full Text: DOI arXiv
Selivanova, N. Yu.; Shamolin, M. V. Studying the interphase zone in a certain singular-limit problem. (English. Russian original) Zbl 1321.35172 J. Math. Sci., New York 189, No. 2, 284-293 (2013); translation from Sovrem. Mat. Prilozh. 78 (2012). Reviewer: Thomas Hagen (Memphis) MSC: 35Q35 35R35 35B40 80A22 PDFBibTeX XMLCite \textit{N. Yu. Selivanova} and \textit{M. V. Shamolin}, J. Math. Sci., New York 189, No. 2, 284--293 (2013; Zbl 1321.35172); translation from Sovrem. Mat. Prilozh. 78 (2012) Full Text: DOI
Drábek, Pavel; Robinson, Stephen B. Continua of local minimizers in a non-smooth model of phase transitions. (English) Zbl 1264.74185 Z. Angew. Math. Phys. 62, No. 4, 609-622 (2011). MSC: 74N99 74G65 PDFBibTeX XMLCite \textit{P. Drábek} and \textit{S. B. Robinson}, Z. Angew. Math. Phys. 62, No. 4, 609--622 (2011; Zbl 1264.74185) Full Text: DOI
Chamard, Jeremy; Otta, Josef; Lloyd, David J. B. Computation of minimum energy paths for quasi-linear problems. (English) Zbl 1245.65071 J. Sci. Comput. 49, No. 2, 180-194 (2011). MSC: 65K10 PDFBibTeX XMLCite \textit{J. Chamard} et al., J. Sci. Comput. 49, No. 2, 180--194 (2011; Zbl 1245.65071) Full Text: DOI Link
Zhao, Kun Global regularity for a coupled Cahn-Hilliard-Boussinesq system on bounded domains. (English) Zbl 1219.35199 Q. Appl. Math. 69, No. 2, 331-356 (2011). MSC: 35Q35 35B65 35B40 PDFBibTeX XMLCite \textit{K. Zhao}, Q. Appl. Math. 69, No. 2, 331--356 (2011; Zbl 1219.35199) Full Text: DOI Link
Bethuel, Fabrice; Orlandi, Giandomenico; Smets, Didier Slow motion for gradient systems with equal depth multiple-well potentials. (English) Zbl 1213.35254 J. Differ. Equations 250, No. 1, 53-94 (2011). Reviewer: Jiaqi Mo (Wuhu) MSC: 35K57 35K15 PDFBibTeX XMLCite \textit{F. Bethuel} et al., J. Differ. Equations 250, No. 1, 53--94 (2011; Zbl 1213.35254) Full Text: DOI arXiv
Kitavtsev, Georgy; Wagner, Barbara Coarsening dynamics of slipping droplets. (English) Zbl 1188.76191 J. Eng. Math. 66, No. 1-3, 271-292 (2010). MSC: 76A20 76D08 PDFBibTeX XMLCite \textit{G. Kitavtsev} and \textit{B. Wagner}, J. Eng. Math. 66, No. 1--3, 271--292 (2010; Zbl 1188.76191) Full Text: DOI Link
Dehghan, Mehdi; Mirzaei, Davoud A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn-Hilliard equation. (English) Zbl 1244.74149 Eng. Anal. Bound. Elem. 33, No. 4, 522-528 (2009). MSC: 74S15 74N99 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{D. Mirzaei}, Eng. Anal. Bound. Elem. 33, No. 4, 522--528 (2009; Zbl 1244.74149) Full Text: DOI
Bates, Peter W.; Lu, Kening; Zeng, Chongchun Approximately invariant manifolds and global dynamics of spike states. (English) Zbl 1157.37013 Invent. Math. 174, No. 2, 355-433 (2008). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37D10 37L25 35K55 58J10 PDFBibTeX XMLCite \textit{P. W. Bates} et al., Invent. Math. 174, No. 2, 355--433 (2008; Zbl 1157.37013) Full Text: DOI
Ward, Michael J. Asymptotic methods for reaction-diffusion systems: past and present. (English) Zbl 1334.92004 Bull. Math. Biol. 68, No. 5, 1151-1167 (2006). MSC: 92-03 92C45 92C40 PDFBibTeX XMLCite \textit{M. J. Ward}, Bull. Math. Biol. 68, No. 5, 1151--1167 (2006; Zbl 1334.92004) Full Text: DOI
Ishimura, Naoyuki; Nakamura, Ken-Ichi; Nakamura, Masaaki Bifurcations of steady states for the Eguchi–Oki–Matsumura model of phase separation. (English) Zbl 1136.80307 Appl. Anal. 85, No. 6-7, 831-843 (2006). MSC: 80A30 37C75 35K45 PDFBibTeX XMLCite \textit{N. Ishimura} et al., Appl. Anal. 85, No. 6--7, 831--843 (2006; Zbl 1136.80307) Full Text: DOI
Ye, Xingde; Cheng, Xiaoliang The Fourier spectral method for the Cahn-Hilliard equation. (English) Zbl 1093.65099 Appl. Math. Comput. 171, No. 1, 345-357 (2005). Reviewer: Song Jiang (Beijing) MSC: 65M70 65M15 65M12 35Q72 35K35 PDFBibTeX XMLCite \textit{X. Ye} and \textit{X. Cheng}, Appl. Math. Comput. 171, No. 1, 345--357 (2005; Zbl 1093.65099) Full Text: DOI
Potapov, A. B.; Hillen, T. Metastability in chemotaxis models. (English) Zbl 1170.35460 J. Dyn. Differ. Equations 17, No. 2, 293-330 (2005). MSC: 35K57 37L10 92C17 PDFBibTeX XMLCite \textit{A. B. Potapov} and \textit{T. Hillen}, J. Dyn. Differ. Equations 17, No. 2, 293--330 (2005; Zbl 1170.35460) Full Text: DOI
Bates, Peter W.; Han, Jianlong The Dirichlet boundary problem for a nonlocal Cahn-Hilliard equation. (English) Zbl 1108.45004 J. Math. Anal. Appl. 311, No. 1, 289-312 (2005). Reviewer: Anatoliy Aleksandrovich Kilbas (Minsk) MSC: 45K05 35K55 35Q53 PDFBibTeX XMLCite \textit{P. W. Bates} and \textit{J. Han}, J. Math. Anal. Appl. 311, No. 1, 289--312 (2005; Zbl 1108.45004) Full Text: DOI
Bates, Peter W.; Han, Jianlong The Neumann boundary problem for a nonlocal Cahn-Hilliard equation. (English) Zbl 1081.45004 J. Differ. Equations 212, No. 2, 235-277 (2005). Reviewer: Mohamed O. El-Doma (Beirut) MSC: 45K05 45M05 45G10 PDFBibTeX XMLCite \textit{P. W. Bates} and \textit{J. Han}, J. Differ. Equations 212, No. 2, 235--277 (2005; Zbl 1081.45004) Full Text: DOI
Chen, Xinfu Generation, propagation, and annihilation of metastable patterns. (English) Zbl 1061.35014 J. Differ. Equations 206, No. 2, 399-437 (2004). Reviewer: Jiaqi Mo (Wuhu) MSC: 35B25 35K57 37L99 74N99 PDFBibTeX XMLCite \textit{X. Chen}, J. Differ. Equations 206, No. 2, 399--437 (2004; Zbl 1061.35014) Full Text: DOI
Ye, Xingde The Legendre collocation method for the Cahn–Hilliard equation. (English) Zbl 1043.65116 J. Comput. Appl. Math. 150, No. 1, 87-108 (2003). Reviewer: Eric Sonnendrücker (Strasbourg) MSC: 65M70 65M12 35Q53 PDFBibTeX XMLCite \textit{X. Ye}, J. Comput. Appl. Math. 150, No. 1, 87--108 (2003; Zbl 1043.65116) Full Text: DOI
Wang, Xuefeng Metastability and stability of patterns in a convolution model for phase transitions. (English) Zbl 1011.35073 J. Differ. Equations 183, No. 2, 434-461 (2002). Reviewer: Chuangan Hu (Tianjin) MSC: 35K55 35B25 58E50 PDFBibTeX XMLCite \textit{X. Wang}, J. Differ. Equations 183, No. 2, 434--461 (2002; Zbl 1011.35073) Full Text: DOI
Ye, Xingde The Fourier collocation method for the Cahn-Hilliard equation. (English) Zbl 1034.65085 Comput. Math. Appl. 44, No. 1-2, 213-229 (2002). Reviewer: Mária Lukáčová (Hamburg) MSC: 65M70 65M15 PDFBibTeX XMLCite \textit{X. Ye}, Comput. Math. Appl. 44, No. 1--2, 213--229 (2002; Zbl 1034.65085) Full Text: DOI
Shi, Junping Semilinear Neumann boundary value problems on a rectangle. (English) Zbl 0992.35031 Trans. Am. Math. Soc. 354, No. 8, 3117-3154 (2002). MSC: 35J25 35J60 34C11 35B32 PDFBibTeX XMLCite \textit{J. Shi}, Trans. Am. Math. Soc. 354, No. 8, 3117--3154 (2002; Zbl 0992.35031) Full Text: DOI
de Groen, P. P. N.; Karadzhov, G. E. Slow travelling waves on a finite interval for Burgers’-type equations. (English) Zbl 0986.35094 J. Comput. Appl. Math. 132, No. 1, 155-189 (2001). MSC: 35Q53 35B25 35K60 PDFBibTeX XMLCite \textit{P. P. N. de Groen} and \textit{G. E. Karadzhov}, J. Comput. Appl. Math. 132, No. 1, 155--189 (2001; Zbl 0986.35094) Full Text: DOI
Pinto, João T. Slow motion manifolds far from the attractor in multistable reaction-diffusion equations. (English) Zbl 0986.35048 J. Differ. Equations 174, No. 1, 101-132 (2001). Reviewer: Jan Cholewa (Katowice) MSC: 35K57 PDFBibTeX XMLCite \textit{J. T. Pinto}, J. Differ. Equations 174, No. 1, 101--132 (2001; Zbl 0986.35048) Full Text: DOI
Boyer, Franck Nonhomogeneous Cahn-Hilliard fluids. (English) Zbl 1037.76062 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18, No. 2, 225-259 (2001). MSC: 76T99 76D05 35Q35 PDFBibTeX XMLCite \textit{F. Boyer}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18, No. 2, 225--259 (2001; Zbl 1037.76062) Full Text: DOI Numdam EuDML
Kalies, William D.; VanderVorst, Robert C. A. M.; Wanner, Thomas Slow motion in higher-order systems and \(\Gamma\)-convergence in one space dimension. (English) Zbl 0976.35005 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 44, No. 1, 33-57 (2001). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K60 35A15 37C29 PDFBibTeX XMLCite \textit{W. D. Kalies} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 44, No. 1, 33--57 (2001; Zbl 0976.35005) Full Text: DOI
Bates, Peter W.; Fusco, Giorgio Equilibria with many nuclei for the Cahn-Hilliard equation. (English) Zbl 0990.35016 J. Differ. Equations 160, No. 2, 283-356 (2000). Reviewer: Michael Grinfeld (Glasgow) MSC: 35B25 35K35 35K55 35B05 37N15 PDFBibTeX XMLCite \textit{P. W. Bates} and \textit{G. Fusco}, J. Differ. Equations 160, No. 2, 283--356 (2000; Zbl 0990.35016) Full Text: DOI
Novick-Cohen, A. Triple-junction motion for an Allen-Cahn/Cahn-Hilliard system. (English) Zbl 0954.35081 Physica D 137, No. 1-2, 1-24 (2000). Reviewer: Alina Stancu (Villeneuve D’Ascq) MSC: 35K40 74N20 35K90 PDFBibTeX XMLCite \textit{A. Novick-Cohen}, Physica D 137, No. 1--2, 1--24 (2000; Zbl 0954.35081) Full Text: DOI
Kowalczyk, Michał Multiple spike layers in the shadow Gierer-Meinhardt system: Existence of equilibria and the quasi-invariant manifold. (English) Zbl 0962.35063 Duke Math. J. 98, No. 1, 59-111 (1999). Reviewer: Jiaqi Mo (Wuhu) MSC: 35J65 35B25 35C20 92C15 PDFBibTeX XMLCite \textit{M. Kowalczyk}, Duke Math. J. 98, No. 1, 59--111 (1999; Zbl 0962.35063) Full Text: DOI
Rybka, Piotr; Hoffmann, Karl-Heinz Convergence of solutions to Cahn-Hilliard equation. (English) Zbl 0936.35032 Commun. Partial Differ. Equations 24, No. 5-6, 1055-1077 (1999). Reviewer: Marianne Korten (Warszawa) MSC: 35B40 35K60 35K35 PDFBibTeX XMLCite \textit{P. Rybka} and \textit{K.-H. Hoffmann}, Commun. Partial Differ. Equations 24, No. 5--6, 1055--1077 (1999; Zbl 0936.35032) Full Text: DOI
Grinfeld, M.; Novick-Cohen, A. The viscous Cahn-Hilliard equation: Morse decomposition and structure of the global attractor. (English) Zbl 0927.35045 Trans. Am. Math. Soc. 351, No. 6, 2375-2406 (1999). Reviewer: P.Polacik (Bratislava) MSC: 35K30 37C70 PDFBibTeX XMLCite \textit{M. Grinfeld} and \textit{A. Novick-Cohen}, Trans. Am. Math. Soc. 351, No. 6, 2375--2406 (1999; Zbl 0927.35045) Full Text: DOI
Golovin, A. A.; Davis, S. H.; Nepomnyashchy, A. A. A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth. (English) Zbl 0952.74050 Physica D 122, No. 1-4, 202-230 (1998). MSC: 74N05 74E15 74H40 82D25 80A22 PDFBibTeX XMLCite \textit{A. A. Golovin} et al., Physica D 122, No. 1--4, 202--230 (1998; Zbl 0952.74050) Full Text: DOI
Li, Desheng; Zhong, Chenkui Global attractor for the Cahn-Hilliard system with fast growing nonlinearity. (English) Zbl 0912.35029 J. Differ. Equations 149, No. 2, 191-210 (1998). Reviewer: Lubomira Softova (Sofia) MSC: 35B40 35K50 37C70 PDFBibTeX XMLCite \textit{D. Li} and \textit{C. Zhong}, J. Differ. Equations 149, No. 2, 191--210 (1998; Zbl 0912.35029) Full Text: DOI
Wei, Juncheng; Winter, Matthias On the stationary Cahn-Hilliard equation: Interior spike solutions. (English) Zbl 0965.35070 J. Differ. Equations 148, No. 2, 231-267 (1998). MSC: 35J65 35B25 35J60 PDFBibTeX XMLCite \textit{J. Wei} and \textit{M. Winter}, J. Differ. Equations 148, No. 2, 231--267 (1998; Zbl 0965.35070) Full Text: DOI
Wei, Juncheng; Winter, Matthias Stationary solutions for the Cahn-Hilliard equation. (English) Zbl 0910.35049 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 15, No. 4, 459-492 (1998). Reviewer: I.Ginchev (Varna) MSC: 35J65 35B05 35B40 PDFBibTeX XMLCite \textit{J. Wei} and \textit{M. Winter}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 15, No. 4, 459--492 (1998; Zbl 0910.35049) Full Text: DOI Numdam EuDML
Ohnishi, Isamu; Nishiura, Yasumasa Spectral comparison between the second and the fourth order equations of conservative type with non-local terms. (English) Zbl 0905.35009 Japan J. Ind. Appl. Math. 15, No. 2, 253-262 (1998). MSC: 35B05 35J65 35B35 35P05 PDFBibTeX XMLCite \textit{I. Ohnishi} and \textit{Y. Nishiura}, Japan J. Ind. Appl. Math. 15, No. 2, 253--262 (1998; Zbl 0905.35009) Full Text: DOI
Danilov, V. G.; Omel’yanov, G. A.; Radkevich, E. V. Asymptotic solutions of the Cahn-Hilliard system in the fast relaxation case. (English. Russian original) Zbl 0983.35054 J. Math. Sci., New York 97, No. 3, 4027-4044 (1999); translation from Tr. Semin. Im. I. G. Petrovskogo 20, 48-80 (1997). Reviewer: Vladimir Ďurikovič (Bratislava) MSC: 35K50 35B35 PDFBibTeX XMLCite \textit{V. G. Danilov} et al., J. Math. Sci., New York 97, No. 3, 4027--4044 (1997; Zbl 0983.35054); translation from Tr. Semin. Im. I. G. Petrovskogo 20, 48--80 (1997) Full Text: DOI
Soner, Halil Mete Ginzburg-Landau equation and motion by mean curvature. I: Convergence. (English) Zbl 0935.35060 J. Geom. Anal. 7, No. 3, 437-475 (1997). Reviewer: Vicentiu D.Rădulescu (Craiova) MSC: 35K55 35B25 PDFBibTeX XMLCite \textit{H. M. Soner}, J. Geom. Anal. 7, No. 3, 437--475 (1997; Zbl 0935.35060) Full Text: DOI
Kowalczyk, Michał Exponentially slow dynamics and interfaces intersecting the boundary. (English) Zbl 0892.35081 J. Differ. Equations 138, No. 1, 55-85 (1997). Reviewer: S.Jimbo (Sapporo) MSC: 35K60 35B25 PDFBibTeX XMLCite \textit{M. Kowalczyk}, J. Differ. Equations 138, No. 1, 55--85 (1997; Zbl 0892.35081) Full Text: DOI
Cahn, J. W.; Elliott, C. M.; Novick-Cohen, A. The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature. (English) Zbl 0861.35039 Eur. J. Appl. Math. 7, No. 3, 287-301 (1996). MSC: 35K55 PDFBibTeX XMLCite \textit{J. W. Cahn} et al., Eur. J. Appl. Math. 7, No. 3, 287--301 (1996; Zbl 0861.35039) Full Text: DOI
Novick-Cohen, A.; Zheng, Songmu The Penrose-Fife-type equations: Counting the one-dimensional stationary solutions. (English) Zbl 0857.35055 Proc. R. Soc. Edinb., Sect. A 126, No. 3, 483-504 (1996). MSC: 35K50 35K55 PDFBibTeX XMLCite \textit{A. Novick-Cohen} and \textit{S. Zheng}, Proc. R. Soc. Edinb., Sect. A, Math. 126, No. 3, 483--504 (1996; Zbl 0857.35055) Full Text: DOI
Friesecke, G.; McLeod, J. B. Dynamics as a mechanism preventing the formation of finer and fine microstructure. (English) Zbl 0920.73345 Arch. Ration. Mech. Anal. 133, No. 3, 199-247 (1996). MSC: 74A60 74M25 35Q72 PDFBibTeX XMLCite \textit{G. Friesecke} and \textit{J. B. McLeod}, Arch. Ration. Mech. Anal. 133, No. 3, 199--247 (1996; Zbl 0920.73345) Full Text: DOI
Lin, Xiao-Biao Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system. (English) Zbl 0852.35012 Trans. Am. Math. Soc. 348, No. 2, 713-753 (1996). Reviewer: V.N.Grebenev (Novosibirsk) MSC: 35B25 35K57 35C20 PDFBibTeX XMLCite \textit{X.-B. Lin}, Trans. Am. Math. Soc. 348, No. 2, 713--753 (1996; Zbl 0852.35012) Full Text: DOI arXiv
Vishnevskij, M. P.; Zelenyak, T. I.; Lavrent’ev, M. M. jun. Behavior of solutions to nonlinear parabolic equations at large time. (English. Russian original) Zbl 0863.35051 Sib. Math. J. 36, No. 3, 435-453 (1995); translation from Sib. Mat. Zh. 36, No. 3, 510-530 (1995). Reviewer: P.Polacik (Bratislava) MSC: 35K60 35B40 35B05 35B35 PDFBibTeX XMLCite \textit{M. P. Vishnevskij} et al., Sib. Math. J. 36, No. 3, 435--453 (1995; Zbl 0863.35051); translation from Sib. Mat. Zh. 36, No. 3, 510--530 (1995) Full Text: DOI
Grinfeld, M.; Novick-Cohen, A. Counting stationary solutions of the Cahn-Hilliard equation by transversality arguments. (English) Zbl 0828.34007 Proc. R. Soc. Edinb., Sect. A 125, No. 2, 351-370 (1995). Reviewer: N.E.Ratanov (Chelyabinsk) MSC: 34A55 34B15 34C23 82D35 PDFBibTeX XMLCite \textit{M. Grinfeld} and \textit{A. Novick-Cohen}, Proc. R. Soc. Edinb., Sect. A, Math. 125, No. 2, 351--370 (1995; Zbl 0828.34007) Full Text: DOI
Niethammer, Barbara S. Existence and uniqueness of radially symmetric stationary points within the gradient theory of phase transitions. (English) Zbl 0827.35010 Eur. J. Appl. Math. 6, No. 1, 45-67 (1995). MSC: 35B25 35J65 80A22 35J20 35R35 PDFBibTeX XMLCite \textit{B. S. Niethammer}, Eur. J. Appl. Math. 6, No. 1, 45--67 (1995; Zbl 0827.35010) Full Text: DOI
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. (English) Zbl 0828.35105 Arch. Ration. Mech. Anal. 128, No. 2, 165-205 (1994). MSC: 35Q35 35R35 76D99 PDFBibTeX XMLCite \textit{N. D. Alikakos} et al., Arch. Ration. Mech. Anal. 128, No. 2, 165--205 (1994; Zbl 0828.35105) Full Text: DOI
Reyna, Luis G.; Ward, Michael J. Resolving weak internal layer interactions for the Ginzburg-Landau equation. (English) Zbl 0816.35061 Eur. J. Appl. Math. 5, No. 4, 495-523 (1994). MSC: 35K60 65M99 65N99 35B25 PDFBibTeX XMLCite \textit{L. G. Reyna} and \textit{M. J. Ward}, Eur. J. Appl. Math. 5, No. 4, 495--523 (1994; Zbl 0816.35061) Full Text: DOI
Chen, Xinfu Spectrum for the Allen-Cahn, Cahn-Hilliard, and phase-field equations for generic interfaces. (English) Zbl 0811.35098 Commun. Partial Differ. Equations 19, No. 7-8, 1371-1395 (1994). Reviewer: G.Jumarie (Montreal) MSC: 35Q35 35Q55 80A22 35R35 PDFBibTeX XMLCite \textit{X. Chen}, Commun. Partial Differ. Equations 19, No. 7--8, 1371--1395 (1994; Zbl 0811.35098) Full Text: DOI
Ward, Michael J. Metastable patterns, layer collapses, and coarsening for a one- dimensional Ginzburg-Landau equation. (English) Zbl 0794.35119 Stud. Appl. Math. 91, No. 1, 51-93 (1994). MSC: 35Q55 35R35 76V05 PDFBibTeX XMLCite \textit{M. J. Ward}, Stud. Appl. Math. 91, No. 1, 51--93 (1994; Zbl 0794.35119) Full Text: DOI
Kuwamura, Masataka The phase dynamics method with applications to the Swift-Hohenberg equation. (English) Zbl 0797.35015 J. Dyn. Differ. Equations 6, No. 1, 185-225 (1994). Reviewer: A.Steindl (Wien) MSC: 35B40 35B10 76E15 35B32 PDFBibTeX XMLCite \textit{M. Kuwamura}, J. Dyn. Differ. Equations 6, No. 1, 185--225 (1994; Zbl 0797.35015) Full Text: DOI
Bates, Peter W.; Lu, Kening A Hartman-Grobman theorem for the Cahn-Hilliard and phase-field equations. (English) Zbl 0795.35052 J. Dyn. Differ. Equations 6, No. 1, 101-145 (1994). MSC: 35K60 35B30 PDFBibTeX XMLCite \textit{P. W. Bates} and \textit{K. Lu}, J. Dyn. Differ. Equations 6, No. 1, 101--145 (1994; Zbl 0795.35052) Full Text: DOI
Novick-Cohen, A.; Peletier, L. A. Steady states of the one-dimensional Cahn-Hilliard equation. (English) Zbl 0818.35127 Proc. R. Soc. Edinb., Sect. A 123, No. 6, 1071-1098 (1993). MSC: 35Q72 35K55 35R35 35B32 PDFBibTeX XMLCite \textit{A. Novick-Cohen} and \textit{L. A. Peletier}, Proc. R. Soc. Edinb., Sect. A, Math. 123, No. 6, 1071--1098 (1993; Zbl 0818.35127) Full Text: DOI
Novick-Cohen, A.; Peletier, L. A. The steady states of the one-dimensional Cahn-Hilliard equation. (English) Zbl 0770.35036 Appl. Math. Lett. 5, No. 3, 45-46 (1992). MSC: 35K60 35B40 82B26 37D45 PDFBibTeX XMLCite \textit{A. Novick-Cohen} and \textit{L. A. Peletier}, Appl. Math. Lett. 5, No. 3, 45--46 (1992; Zbl 0770.35036) Full Text: DOI
Cessi, Paola; Young, W. R. Multiple equilibria in two-dimensional thermohaline circulation. (English) Zbl 0755.76040 J. Fluid Mech. 241, 291-309 (1992). MSC: 76E20 86A05 PDFBibTeX XMLCite \textit{P. Cessi} and \textit{W. R. Young}, J. Fluid Mech. 241, 291--309 (1992; Zbl 0755.76040) Full Text: DOI
Kuwamura, M.; Ei, S.-I.; Mimura, M. Very slow dynamics for some reaction-diffusion systems of the activator- inhibitor type. (English) Zbl 0767.35038 Japan J. Ind. Appl. Math. 9, No. 1, 35-77 (1992). MSC: 35K57 92D25 92E20 PDFBibTeX XMLCite \textit{M. Kuwamura} et al., Japan J. Ind. Appl. Math. 9, No. 1, 35--77 (1992; Zbl 0767.35038) Full Text: DOI
Fröhlich, Jürg; Struwe, Michael Variational problems on vector bundles. (English) Zbl 0714.58012 Commun. Math. Phys. 131, No. 3, 431-464 (1990). Reviewer: D.Motreanu MSC: 58E30 49J40 81Q05 PDFBibTeX XMLCite \textit{J. Fröhlich} and \textit{M. Struwe}, Commun. Math. Phys. 131, No. 3, 431--464 (1990; Zbl 0714.58012) Full Text: DOI
Bates, Peter W.; Fife, Paul C. Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening. (English) Zbl 0706.58074 Physica D 43, No. 2-3, 335-348 (1990). Reviewer: M.Puta MSC: 58J50 PDFBibTeX XMLCite \textit{P. W. Bates} and \textit{P. C. Fife}, Physica D 43, No. 2--3, 335--348 (1990; Zbl 0706.58074) Full Text: DOI