Author:
Sun Jiebao,Zhang Dazhi,Wu Boying
Abstract
Abstract
This paper considers a kind of degenerate parabolic systems. First, we consider the initial boundary value problem of the two-species degenerate parabolic cooperative system. By using the method of a parabolic regularization and energy estimate, we establish the existence of the weak solution of the problem. Then we establish the comparison principle and discuss the uniqueness and the uniform bound. At last, we consider the periodic boundary value problem of the system. By constructing a pair of ordered upper and lower solutions, we establish the existence of nontrivial nonnegative periodic solutions.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference22 articles.
1. Okubo A Biomathematics 10. In Diffusion and Ecological Problems: Mathematical Models. Springer, Berlin; 1980.
2. Lecture Notes in Mathematics 1936;GF Webb,2008
3. Sun JB: Asymptotic bounds for solutions of a periodic reaction diffusion system. Appl. Math. E-Notes 2010, 10: 128–135.
4. Li JJ, Gao WJ: Global existence and nonexistence for some degenerate and strongly coupled quasilinear parabolic systems. J. Math. Anal. Appl. 2012, 387: 1–7. 10.1016/j.jmaa.2011.05.075
5. Sun JB, Zhang DZ, Wu BY: A two-species cooperative Lotka-Volterra system of degenerate parabolic equations. Abstr. Appl. Anal. 2011., 2011: Article ID 714248
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