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Phase-field systems with vectorial order parameters including diffusional hysteresis effects
1. | Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-chō, Inage-ku, Chiba, 263–8522, Japan |
2. | Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin, Germany |
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Emil Minchev. Existence and uniqueness of solutions of a system of nonlinear PDE for phase transitions with vector order parameter. Conference Publications, 2005, 2005 (Special) : 652-661. doi: 10.3934/proc.2005.2005.652 |
[2] |
Paola Goatin. Traffic flow models with phase transitions on road networks. Networks and Heterogeneous Media, 2009, 4 (2) : 287-301. doi: 10.3934/nhm.2009.4.287 |
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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 |
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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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Shuichi Kawashima, Peicheng Zhu. Traveling waves for models of phase transitions of solids driven by configurational forces. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 309-323. doi: 10.3934/dcdsb.2011.15.309 |
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Dian Palagachev, Lubomira Softova. A priori estimates and precise regularity for parabolic systems with discontinuous data. Discrete and Continuous Dynamical Systems, 2005, 13 (3) : 721-742. doi: 10.3934/dcds.2005.13.721 |
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João-Paulo Dias, Mário Figueira. On the Riemann problem for some discontinuous systems of conservation laws describing phase transitions. Communications on Pure and Applied Analysis, 2004, 3 (1) : 53-58. doi: 10.3934/cpaa.2004.3.53 |
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Shaoqiang Tang, Huijiang Zhao. Stability of Suliciu model for phase transitions. Communications on Pure and Applied Analysis, 2004, 3 (4) : 545-556. doi: 10.3934/cpaa.2004.3.545 |
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Tatyana S. Turova. Structural phase transitions in neural networks. Mathematical Biosciences & Engineering, 2014, 11 (1) : 139-148. doi: 10.3934/mbe.2014.11.139 |
[10] |
Ming Mei, Yau Shu Wong, Liping Liu. Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) Existence and uniform boundedness. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 825-837. doi: 10.3934/dcdsb.2007.7.825 |
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Shu-Yi Zhang. Existence of multidimensional non-isothermal phase transitions in a steady van der Waals flow. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 2221-2239. doi: 10.3934/dcds.2013.33.2221 |
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Sylvie Benzoni-Gavage, Laurent Chupin, Didier Jamet, Julien Vovelle. On a phase field model for solid-liquid phase transitions. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 1997-2025. doi: 10.3934/dcds.2012.32.1997 |
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Valeria Berti, Mauro Fabrizio, Diego Grandi. A phase field model for liquid-vapour phase transitions. Discrete and Continuous Dynamical Systems - S, 2013, 6 (2) : 317-330. doi: 10.3934/dcdss.2013.6.317 |
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Steffen Arnrich. Modelling phase transitions via Young measures. Discrete and Continuous Dynamical Systems - S, 2012, 5 (1) : 29-48. doi: 10.3934/dcdss.2012.5.29 |
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Pavel Drábek, Stephen Robinson. Continua of local minimizers in a quasilinear model of phase transitions. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 163-172. doi: 10.3934/dcds.2013.33.163 |
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Mauro Fabrizio, Claudio Giorgi, Angelo Morro. Isotropic-nematic phase transitions in liquid crystals. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 565-579. doi: 10.3934/dcdss.2011.4.565 |
[17] |
Nicolai T. A. Haydn. Phase transitions in one-dimensional subshifts. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 1965-1973. doi: 10.3934/dcds.2013.33.1965 |
[18] |
James Bremer, Vladimir Rokhlin. Improved estimates for nonoscillatory phase functions. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4101-4131. doi: 10.3934/dcds.2016.36.4101 |
[19] |
Ariane Piovezan Entringer, José Luiz Boldrini. A phase field $\alpha$-Navier-Stokes vesicle-fluid interaction model: Existence and uniqueness of solutions. Discrete and Continuous Dynamical Systems - B, 2015, 20 (2) : 397-422. doi: 10.3934/dcdsb.2015.20.397 |
[20] |
Pavol Quittner, Philippe Souplet. A priori estimates of global solutions of superlinear parabolic problems without variational structure. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1277-1292. doi: 10.3934/dcds.2003.9.1277 |
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