Oulia Bouhoufani, Salim A. Messaoudi, Mostafa Zahri
Abstract:
In this article, we consider a coupled system of two hyperbolic equations with
variable exponents in the damping and source terms, where the dampings are
modilated with time-dependent coefficients \(\alpha(t), \beta(t)\).
First, we state and prove an existence result of a global weak solution,
using Galerkin's method with compactness arguments.
Then, by a Lemma due to Martinez, we establish the decay rates of the solution
energy, under suitable assumptions on the variable exponents \(m\) and \(r\)
and the coefficients \( \alpha\) and \(\beta\).
To illustrate our theoretical results, we give some numerical examples.
Submitted July 29, 2023. Published October 24, 2023.
Math Subject Classifications: 35L05, 35B40, 35L70, 93D20.
Key Words: Coupled system; hyperbolic equation; existence; energy decay; variable-exponent; time-dependent coefficients.
DOI: 10.58997/ejde.2023.73
Show me the PDF file (2424 KB), TEX file for this article.
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Oulia Bouhoufani Department of Mathematics University Batna-2 05000 Batna, Algeria email: o.bouhoufani@univ-batna2.dz |
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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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Mostafa Zahri Mathematics Department University of Sharjah United Arab Emirates email: mzahri@sharjah.ac.ae |
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