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Abstract

The Fujita type global existence and blow-up theorems are proved for a reaction-diffusion system of m equations (m>1) in the form $u_{it} = Δu_i + u_{i+1}^{p_i}, i=1,..., m-1,$ $u_{mt} = Δu_m + u_1^{p_m}, x ∈ ℝ^N, t > 0,$ with nonnegative, bounded, continuous initial values and positive numbers $p_i$. The dependence on $p_i$ of the length of existence time (its finiteness or infinitude) is established.