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On diffusion-induced blowups in a mutualistic model. (English) Zbl 0980.35059

The authors study the effect of diffusion on the blowup of solutions of the semilinear parabolic system

u t =d 1 Δu+u(a 1 -b 1 u+c 1 v)inΩ×(0,T * ),v t =d 2 Δv+v(a 2 -b 2 u-c 2 v)inΩ×(0,T * ),u/ν=v/ν=0onΩ×(0,T * ),u(x,0)=u 0 (x),v(x,0)=v 0 (x)inΩ ¯,

with a bounded and smooth domain Ω n and T * being the maximal existence time of the solution.

MSC:
35K50Systems of parabolic equations, boundary value problems (MSC2000)
92D40Ecology
35B40Asymptotic behavior of solutions of PDE
35K57Reaction-diffusion equations