Affiliation:
1. School of Sciences, Nantong University, Nantong 226019, China
Abstract
This article mainly deals with the blow-up properties of nonnegative solutions for a reaction–diffusion system coupled with norm-type sources under positive boundary value conditions. The local existence of a nonnegative solution and the comparison principle are given. The criteria for the global existence or finite time blow-up of the solutions are obtained by constructing new functions and utilizing the super- and -sub-solution method. The results reveal a correlation between the blow-up profiles of the solutions and the size of the domain, as well as the positive boundary value.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference33 articles.
1. On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium;Diaz;J. Differ. Equ.,1987
2. Vázquez, J.L. (2007). The Porous Medium Equation: Mathematical Theory, Oxford University Press.
3. Blowing-up of solution for a nonlocal reaction-diffusion problem in combustion theory;Pao;J. Math. Anal. App.,1992
4. Uniform blow-up profile for a degenerate parabolic system with nonlocal source;Duan;Comput. Math. Appl.,2004
5. Meinhardt, H. (1982). Models of Biological Pattern Formation, Academic Press.