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
Show me the PDF file (960 KB), TEX file for this article.
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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 |
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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 | |
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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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