Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions
Permanent link to this recordhttp://hdl.handle.net/10754/575570
MetadataShow full item record
AbstractThe 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.
CitationGerbi, S., & Said-Houari, B. (2013). Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions. Advances in Nonlinear Analysis, 0(0). doi:10.1515/anona-2012-0027
PublisherWalter de Gruyter GmbH
JournalAdvances in Nonlinear Analysis