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On the traveling wave solutions for a nonlinear diffusionconvection 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) : 10991115. doi: 10.3934/cpaa.2010.9.1099 
[2] 
Jiao Chen, Weike Wang. The pointwise estimates for the solution of damped wave equation with nonlinear convection in multidimensional space. Communications on Pure and Applied Analysis, 2014, 13 (1) : 307330. doi: 10.3934/cpaa.2014.13.307 
[3] 
Anton S. Zadorin. Exact travelling solution for a reactiondiffusion system with a piecewise constant production supported by a codimension1 subspace. Communications on Pure and Applied Analysis, 2022, 21 (5) : 15671580. doi: 10.3934/cpaa.2022030 
[4] 
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) : 607649. doi: 10.3934/dcds.2011.31.607 
[5] 
Zhaosheng Feng, Qingguo Meng. Exact solution for a twodimensional KDVBurgerstype equation with nonlinear terms of any order. Discrete and Continuous Dynamical Systems  B, 2007, 7 (2) : 285291. doi: 10.3934/dcdsb.2007.7.285 
[6] 
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) : 8393. doi: 10.3934/mfc.2019007 
[7] 
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) : 22132227. doi: 10.3934/cpaa.2013.12.2213 
[8] 
Dominika Pilarczyk. Asymptotic stability of singular solution to nonlinear heat equation. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 9911001. doi: 10.3934/dcds.2009.25.991 
[9] 
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) : 5562. doi: 10.3934/jimo.2006.2.55 
[10] 
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) : 21492165. doi: 10.3934/dcdss.2016089 
[11] 
Feng Li, Yuxiang Li. Global existence of weak solution in a chemotaxisfluid system with nonlinear diffusion and rotational flux. Discrete and Continuous Dynamical Systems  B, 2019, 24 (10) : 54095436. doi: 10.3934/dcdsb.2019064 
[12] 
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) : 487498. doi: 10.3934/cpaa.2005.4.487 
[13] 
JongShenq Guo, YingChih Lin. Traveling wave solution for a lattice dynamical system with convolution type nonlinearity. Discrete and Continuous Dynamical Systems, 2012, 32 (1) : 101124. doi: 10.3934/dcds.2012.32.101 
[14] 
Jifeng Chu, Delia IonescuKruse, Yanjuan Yang. Exact solution and instability for geophysical waves at arbitrary latitude. Discrete and Continuous Dynamical Systems, 2019, 39 (8) : 43994414. doi: 10.3934/dcds.2019178 
[15] 
Fahe Miao, Michal Fečkan, Jinrong Wang. Exact solution and instability for geophysical edge waves. Communications on Pure and Applied Analysis, 2022, 21 (7) : 24472461. doi: 10.3934/cpaa.2022067 
[16] 
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) : 191219. doi: 10.3934/cpaa.2002.1.191 
[17] 
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) : 653658. doi: 10.3934/dcds.2009.24.653 
[18] 
Guofu Lu. Nonexistence and short time asymptotic behavior of sourcetype solution for porous medium equation with convection in onedimension. Discrete and Continuous Dynamical Systems  B, 2016, 21 (5) : 15671586. 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) : 407419. 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) : 54735508. doi: 10.3934/dcds.2021085 
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