Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions

Advances in Nonlinear Analysis

article

Stéphane Gerbi¹  Belkacem Said-Houari² 

[1] Laboratoire de Mathématiques, Université de Savoie et CNRS;Division of Mathematical and Computer Sciences and Engineering, King Abdullah University of Science and Technology (KAUST)

关键词: Damped viscoelastic wave equations;    global solutions;    exponential growth;    blow up in finite time;    dynamic boundary conditions;   

DOI  :  10.1515/anona-2012-0027

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Abstract. The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo–Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.

【 授权许可】

CC BY