Comptes Rendus
Partial Differential Equations
The Fujita phenomenon in exterior domains under the Robin boundary conditions
[Le phénomène de Fujita dans un domaine extérieur sous les conditions au bord de Robin]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1059-1061.

Nous utilisons des méthodes de comparaison, comme dans le cas des conditions au bord dynamiques, pour démontrer que le phénomène de Fujita est également vérifié dans un domaine extérieur sous les conditions au bord de Robin.

We use comparison methods, as in the case of the dynamical boundary conditions, to prove that the well-known Fujita phenomenon remains true in an exterior domain of RN under the Robin boundary conditions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.09.006

Jean-Francois Rault 1

1 LMPA FR 2956 CNRS, Université Lille Nord de France, 50, rue F. Buisson, B.P. 699, 62228 Calais cedex, France
@article{CRMATH_2011__349_19-20_1059_0,
     author = {Jean-Francois Rault},
     title = {The {Fujita} phenomenon in exterior domains under the {Robin} boundary conditions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1059--1061},
     publisher = {Elsevier},
     volume = {349},
     number = {19-20},
     year = {2011},
     doi = {10.1016/j.crma.2011.09.006},
     language = {en},
}
TY  - JOUR
AU  - Jean-Francois Rault
TI  - The Fujita phenomenon in exterior domains under the Robin boundary conditions
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 1059
EP  - 1061
VL  - 349
IS  - 19-20
PB  - Elsevier
DO  - 10.1016/j.crma.2011.09.006
LA  - en
ID  - CRMATH_2011__349_19-20_1059_0
ER  - 
%0 Journal Article
%A Jean-Francois Rault
%T The Fujita phenomenon in exterior domains under the Robin boundary conditions
%J Comptes Rendus. Mathématique
%D 2011
%P 1059-1061
%V 349
%N 19-20
%I Elsevier
%R 10.1016/j.crma.2011.09.006
%G en
%F CRMATH_2011__349_19-20_1059_0
Jean-Francois Rault. The Fujita phenomenon in exterior domains under the Robin boundary conditions. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1059-1061. doi : 10.1016/j.crma.2011.09.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.09.006/

[1] C. Bandle; H.A. Levine Fujita type results for convective-like reaction diffusion equations in exterior domains, Z. Angew. Math. Phys., Volume 40 (1989), pp. 665-676

[2] C. Bandle; H.A. Levine On the existence and the nonexistence of global solutions of reaction–diffusion equations in sectorial domains, Trans. Amer. Math. Soc., Volume 316 (1989), pp. 595-622

[3] J. von Below; C. De Coster A qualitative theory for parabolic problems under dynamical boundary conditions, J. Inequal. Appl., Volume 5 (2000), pp. 467-486

[4] A. Constantin; J. Escher Global existence for fully parabolic boundary value problems, NoDEA Nonlinear Differential Equations Appl., Volume 13 (2006), pp. 91-118

[5] H. Fujita On the blowing up of solutions of the Cauchy problem for ut=Δu+u1+α, J. Fac. Sci. Univ. Tokyo, Volume 13 (1966), pp. 109-124

[6] H.A. Levine; Q.S. Zhang The critical Fujita number for a semilinear heat equation in exterior domains with homogeneous Neumann boundary values, Proc. Roy. Soc. Edinburgh Sect. A, Volume 130 (2000), pp. 591-602

[7] K. Mochizuki; R. Suzuki Critical exponent and critical blow up for quasilinear parabolic equations, Israel J. Math., Volume 98 (1997), pp. 141-156

[8] J.-F. Rault The Fujita phenomenon in exterior domains under dynamical boundary conditions, Asymptot. Anal., Volume 66 (2010), pp. 1-8

[9] R. Suzuki Critical blow-up for quasilinear parabolic equations in exterior domains, Tokyo J. Math., Volume 19 (1996), pp. 397-409

[10] F.B. Weissler Existence and nonexistence of global solutions for a semilinear heat equation, Israel J. Math., Volume 38 (1981), pp. 29-40

Cité par Sources :

Commentaires - Politique