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A convexified energy functional for the Fermi-Amaldi correction
The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials
1. | Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, I-20133 Milano |
2. | Laboratoire de Mathématiques et Applications, UMR CNRS 6086, Université de Poitiers - SP2MI, Boulevard Marie et Pierre Curie, F-86962 Chasseneuil Futuroscope Cedex, France |
3. | Università degli Studi di Pavia, Dipartimento di Matematica "F. Casorati", Via Ferrata 1, 27100 Pavia |
[1] |
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 |
[2] |
M. Grasselli, Hana Petzeltová, Giulio Schimperna. Convergence to stationary solutions for a parabolic-hyperbolic phase-field system. Communications on Pure and Applied Analysis, 2006, 5 (4) : 827-838. doi: 10.3934/cpaa.2006.5.827 |
[3] |
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 |
[4] |
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 |
[5] |
Maurizio Grasselli, Giulio Schimperna. Nonlocal phase-field systems with general potentials. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5089-5106. doi: 10.3934/dcds.2013.33.5089 |
[6] |
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 |
[7] |
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 |
[8] |
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 |
[9] |
Stig-Olof Londen, Hana Petzeltová. Convergence of solutions of a non-local phase-field system. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 653-670. doi: 10.3934/dcdss.2011.4.653 |
[10] |
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 |
[11] |
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 |
[12] |
Elena Bonetti, Elisabetta Rocca. Global existence and long-time behaviour for a singular integro-differential phase-field system. Communications on Pure and Applied Analysis, 2007, 6 (2) : 367-387. doi: 10.3934/cpaa.2007.6.367 |
[13] |
Federico Mario Vegni. Dissipativity of a conserved phase-field system with memory. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 949-968. doi: 10.3934/dcds.2003.9.949 |
[14] |
Nobuyuki Kenmochi, Jürgen Sprekels. Phase-field systems with vectorial order parameters including diffusional hysteresis effects. Communications on Pure and Applied Analysis, 2002, 1 (4) : 495-511. doi: 10.3934/cpaa.2002.1.495 |
[15] |
José Luiz Boldrini, Gabriela Planas. A tridimensional phase-field model with convection for phase change of an alloy. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 429-450. doi: 10.3934/dcds.2005.13.429 |
[16] |
Claudio Giorgi. Phase-field models for transition phenomena in materials with hysteresis. Discrete and Continuous Dynamical Systems - S, 2015, 8 (4) : 693-722. doi: 10.3934/dcdss.2015.8.693 |
[17] |
P.K. Galenko, E.V. Abramova, D.M. Herlach. Phase-field study of solute trapping effect in rapid solidification. Conference Publications, 2011, 2011 (Special) : 457-466. doi: 10.3934/proc.2011.2011.457 |
[18] |
Peng Yu, Qiang Du. A variational construction of anisotropic mobility in phase-field simulation. Discrete and Continuous Dynamical Systems - B, 2006, 6 (2) : 391-406. doi: 10.3934/dcdsb.2006.6.391 |
[19] |
Maciek D. Korzec, Hao Wu. Analysis and simulation for an isotropic phase-field model describing grain growth. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 2227-2246. doi: 10.3934/dcdsb.2014.19.2227 |
[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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