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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_am_25_3_313_326,
     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},
     pages = {313--326},
     year = {1999},
     volume = {25},
     number = {3},
     doi = {10.4064/am-25-3-313-326},
     zbl = {1002.35070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am-25-3-313-326/}
}
TY  - JOUR
AU  - Joanna Rencławowicz
TI  - Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations
JO  - Applicationes Mathematicae
PY  - 1999
SP  - 313
EP  - 326
VL  - 25
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am-25-3-313-326/
DO  - 10.4064/am-25-3-313-326
LA  - en
ID  - 10_4064_am_25_3_313_326
ER  - 
%0 Journal Article
%A Joanna Rencławowicz
%T Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations
%J Applicationes Mathematicae
%D 1999
%P 313-326
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/am-25-3-313-326/
%R 10.4064/am-25-3-313-326
%G en
%F 10_4064_am_25_3_313_326
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

Cité par Sources :