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 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.
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Erschienen in
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Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions ; volume:2 ; number:2 ; year:2013 ; pages:163-193
Advances in nonlinear analysis ; 2, Heft 2 (2013), 163-193
- Urheber
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Gerbi, Stéphane
Said-Houari, Belkacem
- DOI
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10.1515/anona-2012-0027
- URN
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urn:nbn:de:101:1-2405011738153.376466679903
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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14.08.2025, 10:53 MESZ
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Beteiligte
- Gerbi, Stéphane
- Said-Houari, Belkacem
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