Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations

Volume 25 / 1998

Joanna Rencławowicz Applicationes Mathematicae 25 (1998), 313-326 DOI: 10.4064/am-25-3-313-326


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.


  • Joanna Rencławowicz

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