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

We consider the initial boundary value problem of the form ut−a Δu=−f(u, v), vt−c Δu−d Δv=+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