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Instability of bound states for 2D nonlinear Schrödinger equations
A tridimensional phase-field model with convection for phase change of an alloy
1. | IMECC-UNICAMP, CP 6065, Campinas-SP, 13081-970, Brazil |
2. | Departamento de Matemática, ICMC-USP, CP 668, São Carlos-SP, 13560-970, Brazil |
[1] |
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 |
[2] |
Denis Danilov, Britta Nestler. Phase-field modelling of nonequilibrium partitioning during rapid solidification in a non-dilute binary alloy. Discrete and Continuous Dynamical Systems, 2006, 15 (4) : 1035-1047. doi: 10.3934/dcds.2006.15.1035 |
[3] |
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 |
[4] |
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 |
[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] |
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 |
[7] |
Tina Hartley, Thomas Wanner. A semi-implicit spectral method for stochastic nonlocal phase-field models. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 399-429. doi: 10.3934/dcds.2009.25.399 |
[8] |
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 |
[9] |
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 |
[10] |
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 |
[11] |
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 |
[12] |
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 |
[13] |
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 |
[14] |
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 |
[15] |
Ahmed Bonfoh, Cyril D. Enyi. Large time behavior of a conserved phase-field system. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1077-1105. doi: 10.3934/cpaa.2016.15.1077 |
[16] |
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 |
[17] |
Bosheng Chen, Huilai Li, Changchun Liu. Optimal distributed control for a coupled phase-field system. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1789-1825. doi: 10.3934/dcdsb.2021110 |
[18] |
Dong Li, Chaoyu Quan, Jiao Xu. Energy-dissipation for time-fractional phase-field equations. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022104 |
[19] |
Maciek Korzec, Andreas Münch, Endre Süli, Barbara Wagner. Anisotropy in wavelet-based phase field models. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1167-1187. doi: 10.3934/dcdsb.2016.21.1167 |
[20] |
Honghu Liu. Phase transitions of a phase field model. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 883-894. doi: 10.3934/dcdsb.2011.16.883 |
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