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Null-exact controllability of a semilinear cascade system of parabolic-hyperbolic equations
Analysis of a variable time-step discretization for a phase transition model with micro-movements
1. | Istituto di Matematica Applicata e Tecnologie Informatiche - CNR, via Ferrata 1, 27100 Pavia, Italy |
[1] |
Jie Jiang, Boling Guo. Asymptotic behavior of solutions to a one-dimensional full model for phase transitions with microscopic movements. Discrete and Continuous Dynamical Systems, 2012, 32 (1) : 167-190. doi: 10.3934/dcds.2012.32.167 |
[2] |
Giovanna Bonfanti, Fabio Luterotti. Global solution to a phase transition model with microscopic movements and accelerations in one space dimension. Communications on Pure and Applied Analysis, 2006, 5 (4) : 763-777. doi: 10.3934/cpaa.2006.5.763 |
[3] |
Pierluigi Colli, Shunsuke Kurima. Time discretization of a nonlinear phase field system in general domains. Communications on Pure and Applied Analysis, 2019, 18 (6) : 3161-3179. doi: 10.3934/cpaa.2019142 |
[4] |
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 |
[5] |
Elena Bonetti, Pierluigi Colli, Mauro Fabrizio, Gianni Gilardi. Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 1001-1026. doi: 10.3934/dcdsb.2006.6.1001 |
[6] |
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 |
[7] |
Tatyana S. Turova. Structural phase transitions in neural networks. Mathematical Biosciences & Engineering, 2014, 11 (1) : 139-148. doi: 10.3934/mbe.2014.11.139 |
[8] |
Mauro Garavello, Benedetto Piccoli. Coupling of microscopic and phase transition models at boundary. Networks and Heterogeneous Media, 2013, 8 (3) : 649-661. doi: 10.3934/nhm.2013.8.649 |
[9] |
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 |
[10] |
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 |
[11] |
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 |
[12] |
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 |
[13] |
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 |
[14] |
Matthieu Hillairet, Alexei Lozinski, Marcela Szopos. On discretization in time in simulations of particulate flows. Discrete and Continuous Dynamical Systems - B, 2011, 15 (4) : 935-956. doi: 10.3934/dcdsb.2011.15.935 |
[15] |
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 |
[16] |
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 |
[17] |
Yinhua Xia, Yan Xu, Chi-Wang Shu. Efficient time discretization for local discontinuous Galerkin methods. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : 677-693. doi: 10.3934/dcdsb.2007.8.677 |
[18] |
Changbing Hu, Kaitai Li. A simple construction of inertial manifolds under time discretization. Discrete and Continuous Dynamical Systems, 1997, 3 (4) : 531-540. doi: 10.3934/dcds.1997.3.531 |
[19] |
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 |
[20] |
Kelum Gajamannage, Erik M. Bollt. Detecting phase transitions in collective behavior using manifold's curvature. Mathematical Biosciences & Engineering, 2017, 14 (2) : 437-453. doi: 10.3934/mbe.2017027 |
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