Generalized result with a unified proof of global existence to a class of reaction‐diffusion systems

Abstract

We prove in this paper a generalized result with a unified proof of global existence in time of classical solutions to a class of a reaction diffusion system with triangular diffusion matrix on a bounded domain in . The system in question is ut=aΔu − f(x,t,u,v), vt=cΔu + dΔv + ρf(x,t,u,v), , t > 0 with f(x,t,0,η) = 0 and f(x,t,ξ,η)≤Kφ(ξ)eση, for all x∈Ω, t > 0, ξ≥0, η≥0; where ρ, K and σ are real positive constants. Copyright © 2016 John Wiley & Sons, Ltd.