The critical Fujita number for a semilinear heat equation in exterior domains with homogeneous Neumann boundary values

H. A. Levine; Q. S. Zhang

doi:10.1017/S0308210500000317

Abstract

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Let D be a domain in Rn with bounded complement and let n ≠ 2. For the initial-boundary value problemwe prove that there are no non-trivial global (non-negative) solutions if 0 < n (p − 1) ≤ 2 and there exist both global non-trivial and non-global solutions if n (p − 1) > 2.

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The critical Fujita number for a semilinear heat equation in exterior domains with homogeneous Neumann boundary values

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