Global existence and energy decay result for a weak viscoelastic wave equations with a dynamic boundary and nonlinear delay term

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• 作者：Mohamed Ferhat ^{ferhat22@hotmail.fr" class="auth_mail" title="E-mail the corresponding author} ; Ali Hakem ; ^{hakemali@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Global existence ; Energy decay ; Source term
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：71
• 期：3
• 页码：779-804
• 全文大小：486 K

文摘

In this paper, we consider the weak viscoelastic wave equation with dynamic boundary conditions, and nonlinear delay term. First, we prove a local existence theorem by using the Faedo–Galerkin approximations combined with a contraction mapping theorem. Secondly, we show that, under suitable conditions on the initial data and the relaxation function, the solution exists globally in time, in using the concept of stable sets. Finally, by exploiting the perturbed Lyapunov functionals, we extend and improve the previous result from Gerbi and Said-Houari (2011).