Electron. J. Differential Equations, Vol. 2021 (2021), No. 91, pp. 1-33.

Existence and blow up in a system of wave equations with nonstandard nonlinearities

Salim A. Messaoudi, Oulia Bouhoufani, Ilhem Hamchi, Mohamed Alahyane

Abstract:
In this article, we consider a coupled system of two nonlinear hyperbolic equations, where the exponents in the damping and source terms are variables. First, we prove a theorem of existence and uniqueness of weak solution, by using the Faedo Galerkin approximations and the Banach fixed oint theorem. Then, using the energy method, we show that certain solutions with positive initial energy blow up in finite time. We also give some numerical applications to illustrate our theoretical results.

Submitted March 16, 2021. Published November 16, 2021.
Math Subject Classifications: 35D30, 35B40, 35B44, 35L70.
Key Words: Hyperbolic system; existence; blow up, variable exponents; nonlinear.
DOI: https://doi.org/10.58997/ejde.2021.91

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Salim A. Messaoudi
Department of Mathematics
University of Sharjah
P. O. Box 27272 Sharjah
United Arab Emirates
email: smessaoudi@sharjah.ac.ae
Oulia Bouhoufani
Department of Mathematics
University Batna-2
05000 Batna, Algeria
email: o.bouhoufani@univ-batna2.dz
  Ilhem Hamchi
Department of Mathematics
University Batna-2
05000 Batna, Algeria
email: i.hamchi@univ-batna2.dz
Mohamed Alahyane
Department of Mathematics, RISE
University of Sharjah
P. O. Box 27272 Sharjah
United Arab Emirates
email: malahyane@sharjah.ac.ae

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