Geodesic
Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations
Applicationes Mathematicae, Tome 25 (1999) no. 3, pp. 313-326

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We examine the parabolic system of three equations $u_t$ - Δu = $v^p$, $v_t$ - Δv = $w^q$, $w_t$ - Δw = $u^r$, x ∈ $ℝ^N$, t > 0 with p, q, r positive numbers, N ≥ 1, and nonnegative, bounded continuous initial values. We obtain global existence and blow up unconditionally (that is, for any initial data). We prove that if pqr ≤ 1 then any solution is global; when pqr > 1 and max(α,β,γ) ≥ N/2 (α, β, γ are defined in terms of p, q, r) then every nontrivial solution exhibits a finite blow up time.
DOI : 10.4064/am-25-3-313-326
Keywords: reaction-diffusion system, global existence, blow up

Joanna Rencławowicz 1

1 
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Joanna Rencławowicz. Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations. Applicationes Mathematicae, Tome 25 (1999) no. 3, pp. 313-326. doi: 10.4064/am-25-3-313-326

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