We consider the initial boundary value problem of the form u(t) - a Delta u = -integral(u, v), v(t) - c Delta u - d Delta v = +integral(u, v), x epsilon Omega epsilon R-N, N greater than or equal to l , t epsilon R* where integral(u, v) greater than or equal to 0, integral(0, V) = 0, v epsilon R; integral(u, v) less than or equal to K phi(u) e(sigma), K and sigma are positive constants, phi(.) is any continuous, nonnegative, locally Lipschitzian function on R such that phi(0) = 0, d > a, and e < d - a with bounded continuous nonegative initial data. This system contains in particular the Frank-Kamenetskii approximation to an nth-order exothermic chemical reaction of Arrhenius type and non-systemically autocatalysed reaction-diffusion systems. We prove the existence of global classical solutions and study their large time behaviour. Our main tools are estimates of the Neumann function for the heat equation and local L-P a priori estimates independent of time. (C) 2000 Academic Press. [References: 20]
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