Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations
Rencławowicz, Joanna
Applicationes Mathematicae, Tome 25 (1998), p. 313-326 / Harvested from The Polish Digital Mathematics Library
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We examine the parabolic system of three equations ut - Δu = vp, vt - Δv = wq, wt - Δw = ur, x ∈ ℝN, 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.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:219206 
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     author = {Joanna Renc\l awowicz},
     title = {Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations},
     journal = {Applicationes Mathematicae},
     volume = {25},
     year = {1998},
     pages = {313-326},
     zbl = {1002.35070},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i3p313bwm}
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Rencławowicz, Joanna. Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations. Applicationes Mathematicae, Tome 25 (1998) pp. 313-326. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i3p313bwm/

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