TY - JOUR
T1 - Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions
AU - Gerbi, Stéphane
AU - Said-Houari, Belkacem
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2013/1/15
Y1 - 2013/1/15
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/575570
UR - https://www.degruyter.com/view/j/anona.ahead-of-print/anona-2012-0027/anona-2012-0027.xml
UR - http://www.scopus.com/inward/record.url?scp=84939641767&partnerID=8YFLogxK
U2 - 10.1515/anona-2012-0027
DO - 10.1515/anona-2012-0027
M3 - Article
SN - 2191-9496
VL - 2
SP - 163
EP - 193
JO - Advances in Nonlinear Analysis
JF - Advances in Nonlinear Analysis
IS - 2
ER -