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

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 inR n . The system in question is u t = a Δ u − f ( x , t , u , v ), v t = c Δ u + d Δ v + ρ f ( x , t , u , v ), x ∈ Ω ⊂ R n ( n ≥ 1 ) , t > 0 with f ( x , t ,0, η ) = 0  and   f ( x , t , ξ , η )≤ K φ ( ξ ) e σ η , 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.