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Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue
1. | Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway, Norway |
[1] |
Erik Grandelius, Kenneth H. Karlsen. The cardiac bidomain model and homogenization. Networks and Heterogeneous Media, 2019, 14 (1) : 173-204. doi: 10.3934/nhm.2019009 |
[2] |
Yong Zeng. Existence and uniqueness of very weak solution of the MHD type system. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 5617-5638. doi: 10.3934/dcds.2020240 |
[3] |
Hassan Khassehkhan, Messoud A. Efendiev, Hermann J. Eberl. A degenerate diffusion-reaction model of an amensalistic biofilm control system: Existence and simulation of solutions. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 371-388. doi: 10.3934/dcdsb.2009.12.371 |
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Michaël Bages, Patrick Martinez. Existence of pulsating waves in a monostable reaction-diffusion system in solid combustion. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 817-869. doi: 10.3934/dcdsb.2010.14.817 |
[5] |
Boris Andreianov, Mostafa Bendahmane, Kenneth H. Karlsen, Charles Pierre. Convergence of discrete duality finite volume schemes for the cardiac bidomain model. Networks and Heterogeneous Media, 2011, 6 (2) : 195-240. doi: 10.3934/nhm.2011.6.195 |
[6] |
Haomin Huang, Mingxin Wang. The reaction-diffusion system for an SIR epidemic model with a free boundary. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2039-2050. doi: 10.3934/dcdsb.2015.20.2039 |
[7] |
Aníbal Rodríguez-Bernal, Alejandro Vidal–López. Existence, uniqueness and attractivity properties of positive complete trajectories for non-autonomous reaction-diffusion problems. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 537-567. doi: 10.3934/dcds.2007.18.537 |
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Alexey Cheskidov, Songsong Lu. The existence and the structure of uniform global attractors for nonautonomous Reaction-Diffusion systems without uniqueness. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 55-66. doi: 10.3934/dcdss.2009.2.55 |
[9] |
Laurent Desvillettes, Michèle Grillot, Philippe Grillot, Simona Mancini. Study of a degenerate reaction-diffusion system arising in particle dynamics with aggregation effects. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4675-4692. doi: 10.3934/dcds.2018205 |
[10] |
Andrea L. Bertozzi, Dejan Slepcev. Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1617-1637. doi: 10.3934/cpaa.2010.9.1617 |
[11] |
Takashi Kajiwara. A Heteroclinic Solution to a Variational Problem Corresponding to FitzHugh-Nagumo type Reaction-Diffusion System with Heterogeneity. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2133-2156. doi: 10.3934/cpaa.2017106 |
[12] |
Anton S. Zadorin. Exact travelling solution for a reaction-diffusion system with a piecewise constant production supported by a codimension-1 subspace. Communications on Pure and Applied Analysis, 2022, 21 (5) : 1567-1580. doi: 10.3934/cpaa.2022030 |
[13] |
Angelo Favini, Atsushi Yagi. Global existence for Laplace reaction-diffusion equations. Discrete and Continuous Dynamical Systems - S, 2020, 13 (5) : 1473-1493. doi: 10.3934/dcdss.2020083 |
[14] |
Dominique Blanchard, Nicolas Bruyère, Olivier Guibé. Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2213-2227. doi: 10.3934/cpaa.2013.12.2213 |
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Karoline Disser. Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 321-330. doi: 10.3934/dcdss.2020326 |
[16] |
Lili Du, Chunlai Mu, Zhaoyin Xiang. Global existence and blow-up to a reaction-diffusion system with nonlinear memory. Communications on Pure and Applied Analysis, 2005, 4 (4) : 721-733. doi: 10.3934/cpaa.2005.4.721 |
[17] |
Shu-Xiang Huang, Fu-Cai Li, Chun-Hong Xie. Global existence and blow-up of solutions to a nonlocal reaction-diffusion system. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 1519-1532. doi: 10.3934/dcds.2003.9.1519 |
[18] |
Hideo Deguchi. A reaction-diffusion system arising in game theory: existence of solutions and spatial dominance. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3891-3901. doi: 10.3934/dcdsb.2017200 |
[19] |
Sebastian Aniţa, William Edward Fitzgibbon, Michel Langlais. Global existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 805-822. doi: 10.3934/dcdsb.2009.11.805 |
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Feng Li, Yuxiang Li. Global existence of weak solution in a chemotaxis-fluid system with nonlinear diffusion and rotational flux. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5409-5436. doi: 10.3934/dcdsb.2019064 |
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