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Inequalities and the Aubry-Mather theory of Hamilton-Jacobi equations
On the asymptotic behavior of the Caginalp system with dynamic boundary conditions
1. | Department of Mathematics, University of Missouri, Columbia, MO, 65211, United States |
2. | Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, I-20133 Milano |
[1] |
Maurizio Grasselli, Hao Wu. Robust exponential attractors for the modified phase-field crystal equation. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2539-2564. doi: 10.3934/dcds.2015.35.2539 |
[2] |
Narcisse Batangouna, Morgan Pierre. Convergence of exponential attractors for a time splitting approximation of the Caginalp phase-field system. Communications on Pure and Applied Analysis, 2018, 17 (1) : 1-19. doi: 10.3934/cpaa.2018001 |
[3] |
S. Gatti, M. Grasselli, V. Pata, M. Squassina. Robust exponential attractors for a family of nonconserved phase-field systems with memory. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 1019-1029. doi: 10.3934/dcds.2005.12.1019 |
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Ciprian G. Gal, Alain Miranville. Robust exponential attractors and convergence to equilibria for non-isothermal Cahn-Hilliard equations with dynamic boundary conditions. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 113-147. doi: 10.3934/dcdss.2009.2.113 |
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A. M. Micheletti, Angela Pistoia. Multiple eigenvalues of the Laplace-Beltrami operator and deformation of the Riemannian metric. Discrete and Continuous Dynamical Systems, 1998, 4 (4) : 709-720. doi: 10.3934/dcds.1998.4.709 |
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Micol Amar, Roberto Gianni. Laplace-Beltrami operator for the heat conduction in polymer coating of electronic devices. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1739-1756. doi: 10.3934/dcdsb.2018078 |
[7] |
Alain Miranville, Costică Moroşanu. Analysis of an iterative scheme of fractional steps type associated to the nonlinear phase-field equation with non-homogeneous dynamic boundary conditions. Discrete and Continuous Dynamical Systems - S, 2016, 9 (2) : 537-556. doi: 10.3934/dcdss.2016011 |
[8] |
Ahmed Bonfoh, Ibrahim A. Suleman. Robust exponential attractors for singularly perturbed conserved phase-field systems with no growth assumption on the nonlinear term. Communications on Pure and Applied Analysis, 2021, 20 (10) : 3655-3682. doi: 10.3934/cpaa.2021125 |
[9] |
Gianluca Mola. Global attractors for a three-dimensional conserved phase-field system with memory. Communications on Pure and Applied Analysis, 2008, 7 (2) : 317-353. doi: 10.3934/cpaa.2008.7.317 |
[10] |
Monica Conti, Stefania Gatti, Alain Miranville. Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 485-505. doi: 10.3934/dcdss.2012.5.485 |
[11] |
Alain Miranville, Elisabetta Rocca, Giulio Schimperna, Antonio Segatti. The Penrose-Fife phase-field model with coupled dynamic boundary conditions. Discrete and Continuous Dynamical Systems, 2014, 34 (10) : 4259-4290. doi: 10.3934/dcds.2014.34.4259 |
[12] |
Maurizio Grasselli, Alain Miranville, Giulio Schimperna. The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 67-98. doi: 10.3934/dcds.2010.28.67 |
[13] |
Andrea Bonito, Roland Glowinski. On the nodal set of the eigenfunctions of the Laplace-Beltrami operator for bounded surfaces in $R^3$: A computational approach. Communications on Pure and Applied Analysis, 2014, 13 (5) : 2115-2126. doi: 10.3934/cpaa.2014.13.2115 |
[14] |
Yoshitsugu Kabeya. Eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a large zonal domain in the unit sphere. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3529-3559. doi: 10.3934/dcds.2020040 |
[15] |
Zhenhua Zhang. Asymptotic behavior of solutions to the phase-field equations with neumann boundary conditions. Communications on Pure and Applied Analysis, 2005, 4 (3) : 683-693. doi: 10.3934/cpaa.2005.4.683 |
[16] |
Jan Bouwe van den Berg, Gabriel William Duchesne, Jean-Philippe Lessard. Rotation invariant patterns for a nonlinear Laplace-Beltrami equation: A Taylor-Chebyshev series approach. Journal of Computational Dynamics, 2022, 9 (2) : 253-278. doi: 10.3934/jcd.2022005 |
[17] |
Jihoon Lee, Vu Manh Toi. Attractors for a class of delayed reaction-diffusion equations with dynamic boundary conditions. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 3135-3152. doi: 10.3934/dcdsb.2020054 |
[18] |
Nobuyuki Kenmochi, Noriaki Yamazaki. Global attractor of the multivalued semigroup associated with a phase-field model of grain boundary motion with constraint. Conference Publications, 2011, 2011 (Special) : 824-833. doi: 10.3934/proc.2011.2011.824 |
[19] |
Sergiu Aizicovici, Hana Petzeltová. Convergence to equilibria of solutions to a conserved Phase-Field system with memory. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 1-16. doi: 10.3934/dcdss.2009.2.1 |
[20] |
Pierluigi Colli, Danielle Hilhorst, Françoise Issard-Roch, Giulio Schimperna. Long time convergence for a class of variational phase-field models. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 63-81. doi: 10.3934/dcds.2009.25.63 |
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