Alan V. Lair

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We show that the reaction-diffusion system u t = ∆ϕ(u) + f (v), v t = ∆ψ(v) + g(u), with homogeneous Neumann boundary conditions, has a positive global solution on Ω × [0,∞) if and only if ∞ ds/ f (F −1 (G(s))) = ∞ (or, equivalently, ∞ ds/g(G −1 (F(s))) = ∞), where F(s) = s 0 f (r)dr and G(s) = s 0 g(r)dr. The domain Ω ⊆ R N (N ≥ 1) is bounded with smooth(More)
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