Comptes Rendus
Wave equation with p(x,t)-Laplacian and damping term: Blow-up of solutions
Comptes Rendus. Mécanique, Volume 339 (2011) no. 12, pp. 751-755.

We study the Dirichlet problem for equation

utt=div(a(x,t)|u|p(x,t)2u)+αut+b(x,t)|u|σ(x,t)2u
in which α is a nonnegative constant, the coefficients a(x,t), b(x,t) and the exponents of nonlinearity p(x,t), σ(x,t) are given functions. Under suitable conditions on the data, we study the finite time blow-up of the solutions.

On considère le problème de Dirichlet pour lʼéquation

utt=div(a(x,t)|u|p(x,t)2u)+αut+b(x,t)|u|σ(x,t)2u
α0 est une constante, a(x,t), b(x,t) sont des coefficients variables et p(x,t),σ(x,t) sont des exposants nonlinéaires. Sous conditions appropriées on étudie le temps fini de blow-up des solutions.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2011.09.001
Keywords: Waves, Nonlinear wave equation, Energy estimates, Variable nonlinearity, Nonstandard growth conditions, Blow-up
Mot clés : Ondes, Équation des ondes nonlinéaire, Estimations énergétiques, Nonlinéarités variables, Croissance non standard, Blow-up

Stanislav Antontsev 1

1 CMAF, University of Lisbon, Av. Prof. Gama Pinto, 2, 1649-003 Lisbon, Portugal
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Stanislav Antontsev. Wave equation with $ p(x,t)$-Laplacian and damping term: Blow-up of solutions. Comptes Rendus. Mécanique, Volume 339 (2011) no. 12, pp. 751-755. doi : 10.1016/j.crme.2011.09.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.09.001/

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