Author:
Bouhoufani Oulia,Messaoudi Salim A.,Zahri Mostafa
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.
For more information see https://ejde.math.txstate.edu/Volumes/2023/73/abstr.html
Reference31 articles.
1. Aboulaich, R.; Meskin, D.; Souissi, A.; New diffusion models in image processing, Comput. Math. App., 56 (4) (2008), 874-882.
2. Agre, K.; Rammaha, M.; Systems of nonlinear wave equations with damping and source terms, Differential Integral Equations, 19 (2006), 1235-1270.
3. Antontsev, S.; Shmarev, S.; Evolution PDEs with Nonstandard Growth Conditions, Series Editor: Michel Chipot.
4. Antontsev, S.; Wave equation with p(x, t)-Laplacian and damping term: Existence and blow- up, J. Difference Equ. Appl., 3 (2011), 503-525.
5. Benaissa, A.; Mimiouni, S.; Energy decay of solutions of a wave equation of p−Laplacian type with a weakly nonlinear dissipation, Journal of Inequalities in Pure and Applied Mathematics, 7 (2006), Issue 1, Article 15, 1-8.