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

Stéphane Gerbi, Belkacem Said-Houari

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)163-193
Number of pages31
JournalAdvances in Nonlinear Analysis
Volume2
Issue number2
DOIs
StatePublished - Jan 15 2013

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