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, Tome 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.

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DOI : 10.1016/j.crma.2011.09.006
Rault, Jean-Francois 1

1 LMPA FR 2956 CNRS, Université Lille Nord de France, 50, rue F. Buisson, B.P. 699, 62228 Calais cedex, France
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Rault, Jean-Francois. The Fujita phenomenon in exterior domains under the Robin boundary conditions. Comptes Rendus. Mathématique, Tome 349 (2011) no. 19-20, pp. 1059-1061. doi : 10.1016/j.crma.2011.09.006. http://www.numdam.org/articles/10.1016/j.crma.2011.09.006/

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

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

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

[5] Fujita, H. 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] Levine, H.A.; Zhang, Q.S. 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] Mochizuki, K.; Suzuki, R. Critical exponent and critical blow up for quasilinear parabolic equations, Israel J. Math., Volume 98 (1997), pp. 141-156

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

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

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

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