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Behavior of the life span for solutions to the system of reaction-diffusion equations. (English) Zbl 1050.35031

The author studies the following reaction-diffusion systems

t u=Δu+a(x)v p , t v=Δv+b(x)u q

in the total space N · Conditions for the existence, blow-up and global existence of solutions to the above systems in terms of the growth as x of the functions a(x),b(x) and the initial data u 0 ,v 0 are given.

MSC:
35K45Systems of second-order parabolic equations, initial value problems
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35K57Reaction-diffusion equations
Keywords:
existence; blow-up