Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2013-05-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2012-0027 |
| Summary: | 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. |
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| ISSN: | 2191-9496 2191-950X |