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On the traveling wave solutions for a nonlinear diffusion-convection equation: Dynamical system approach
1. | Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004 |
[1] |
Út V. Lê. Regularity of the solution of a nonlinear wave equation. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1099-1115. doi: 10.3934/cpaa.2010.9.1099 |
[2] |
Jiao Chen, Weike Wang. The point-wise estimates for the solution of damped wave equation with nonlinear convection in multi-dimensional space. Communications on Pure and Applied Analysis, 2014, 13 (1) : 307-330. doi: 10.3934/cpaa.2014.13.307 |
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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 |
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Oana Pocovnicu. Explicit formula for the solution of the Szegö equation on the real line and applications. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 607-649. doi: 10.3934/dcds.2011.31.607 |
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Zhaosheng Feng, Qingguo Meng. Exact solution for a two-dimensional KDV-Burgers-type equation with nonlinear terms of any order. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 285-291. doi: 10.3934/dcdsb.2007.7.285 |
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Aleksa Srdanov, Radiša Stefanović, Aleksandra Janković, Dragan Milovanović. "Reducing the number of dimensions of the possible solution space" as a method for finding the exact solution of a system with a large number of unknowns. Mathematical Foundations of Computing, 2019, 2 (2) : 83-93. doi: 10.3934/mfc.2019007 |
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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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Dominika Pilarczyk. Asymptotic stability of singular solution to nonlinear heat equation. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 991-1001. doi: 10.3934/dcds.2009.25.991 |
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V.N. Malozemov, A.V. Omelchenko. On a discrete optimal control problem with an explicit solution. Journal of Industrial and Management Optimization, 2006, 2 (1) : 55-62. doi: 10.3934/jimo.2006.2.55 |
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Xue Yang, Xinglong Wu. Wave breaking and persistent decay of solution to a shallow water wave equation. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2149-2165. doi: 10.3934/dcdss.2016089 |
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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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Claudianor O. Alves. Existence of periodic solution for a class of systems involving nonlinear wave equations. Communications on Pure and Applied Analysis, 2005, 4 (3) : 487-498. doi: 10.3934/cpaa.2005.4.487 |
[13] |
Jong-Shenq Guo, Ying-Chih Lin. Traveling wave solution for a lattice dynamical system with convolution type nonlinearity. Discrete and Continuous Dynamical Systems, 2012, 32 (1) : 101-124. doi: 10.3934/dcds.2012.32.101 |
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Jifeng Chu, Delia Ionescu-Kruse, Yanjuan Yang. Exact solution and instability for geophysical waves at arbitrary latitude. Discrete and Continuous Dynamical Systems, 2019, 39 (8) : 4399-4414. doi: 10.3934/dcds.2019178 |
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Fahe Miao, Michal Fečkan, Jinrong Wang. Exact solution and instability for geophysical edge waves. Communications on Pure and Applied Analysis, 2022, 21 (7) : 2447-2461. doi: 10.3934/cpaa.2022067 |
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Alain Hertzog, Antoine Mondoloni. Existence of a weak solution for a quasilinear wave equation with boundary condition. Communications on Pure and Applied Analysis, 2002, 1 (2) : 191-219. doi: 10.3934/cpaa.2002.1.191 |
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José F. Caicedo, Alfonso Castro. A semilinear wave equation with smooth data and no resonance having no continuous solution. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 653-658. doi: 10.3934/dcds.2009.24.653 |
[18] |
Guofu Lu. Nonexistence and short time asymptotic behavior of source-type solution for porous medium equation with convection in one-dimension. Discrete and Continuous Dynamical Systems - B, 2016, 21 (5) : 1567-1586. doi: 10.3934/dcdsb.2016011 |
[19] |
Bhargav Kumar Kakumani, Suman Kumar Tumuluri. Asymptotic behavior of the solution of a diffusion equation with nonlocal boundary conditions. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 407-419. doi: 10.3934/dcdsb.2017019 |
[20] |
Kin Ming Hui, Jinwan Park. Asymptotic behaviour of singular solution of the fast diffusion equation in the punctured euclidean space. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5473-5508. doi: 10.3934/dcds.2021085 |
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