A degenerate and strongly coupled quasilinear parabolic system with crosswise diffusion for a mutualistic model

作者：Han, Yuzhu; Gao, Wenjie^*

来源：Nonlinear Analysis: Real World Applications , 2010, 11(5): 3421-3430.

DOI：10.1016/j.nonrwa.2009.12.002

• Crosswise diffusion
• Degenerate
• Strongly coupled
• Global existence
• Global nonexistence

This paper deals with positive solutions of degenerate and strongly coupled quasilinear Parabolic system u(1) = v(alpha) Delta u + u(a(1) -b(1)u(1) +c(1)v(s)), v(t) = u(beta) Delta v +v(a(2) + b(2)u(p) - c(2)v(q)) with null Dirichlet boundary condition describing a cooperating model with crosswise diffusion, where the constants a(i), b(i), c(i) > 0(i = 1,2), alpha, beta >= 0 and l, s, p, q >= 1. Local existence of positive classical solution is proved. Moreover, it will be proved that the solution is global if intra-specific competitions of the species are strong, whereas the solution may be nonglobal if the inter-specific cooperation is strong and 0 < alpha <= s, 0 < beta <= p with alpha, beta < 2.

• 出版日期2010-10
• 单位吉林大学