Author:
Kafini Mohammad, ,Hassan Jamilu Hashim,Al-Gharabli Mohammad M., ,
Abstract
<abstract><p>In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference27 articles.
1. S. Antontsev, S. Shmarev, Evolution PDEs with nonstandard growth conditions: Existence, uniqueness, localization, blow-up, Paris: Atlantis Press, 2015.
2. Y. M. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math., 66 (2006), 1383–1406. doi: 10.1137/050624522.
3. S. Antontsev, V. Zhikov, Higher integrability for parabolic equations of $p(x, t)$-Laplacian type, Adv. Differ. Equ., 10 (2005), 1053–1080.
4. M. Nakao, Decay of solutions of the wave equation with a local nonlinear dissipation, Math. Ann., 305 (1996), 403–417. doi: 10.1007/BF01444231.
5. A. Benaissa, S. A. Messaoudi, Exponential decay of solutions of a nonlinearly damped wave equation, Nonlinear Differ. Equ. Appl., 12 (2006), 391–399. doi: 10.1007/s00030-005-0008-5.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献