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Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations
1998
Applicationes Mathematicae
We examine the parabolic system of three equations 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 (where α, β, γ are defined in terms of p, q, r) then every nontrivial solution exhibits a finite blow up time. 1991 Mathematics Subject Classification: 35B30, 35K55, 35K57.
doi:10.4064/am-25-3-313-326
fatcat:hh46yjfkivechgecot7qruveg4