Global existence and blow-up for a completely coupled Fujita type system

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Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

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_{i t} = Δ u_{i} + u_{i + 1}^{p_{i}}, i = 1, ..., m - 1,

u_{m t} = Δ u_{m} + u_{1}^{p_{m}}, x \in 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.

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