Global Solutions of Reaction-Diffusion Systems with a Balance Law and Nonlinearities of Exponential Growth

Abstract

We consider the initial boundary value problem of the form ut-aΔu=-f(u, v), vt-cΔu-dΔv=+f(u, v), x∈Ω∈RN, N≥1, t∈R+ where f(u, v)≥0, f(0, v)=0, v∈R; f(u, v)≤Kφ(u)eσv, K and σ are positive constants, φ(.) is any continuous, nonnegative, locally Lipschitzian function on R such that φ(0)=0, d>a, and c