Existence and asymptotic behavior of the wave equation with dynamic boundary conditions

Handle URI:
http://hdl.handle.net/10754/562125
Title:
Existence and asymptotic behavior of the wave equation with dynamic boundary conditions
Authors:
Graber, Philip Jameson; Said-Houari, Belkacem
Abstract:
The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Verlag
Journal:
Applied Mathematics and Optimization
Issue Date:
7-Mar-2012
DOI:
10.1007/s00245-012-9165-1
Type:
Article
ISSN:
00954616
Sponsors:
The first author wishes to thank the Virginia Space Grant Consortium and the Jefferson Scholars Foundation for their support. The second author wants to thank KAUST for its support. Both authors are very grateful to Prof. Irena Lasiecka for many fruitful discussions.
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGraber, Philip Jamesonen
dc.contributor.authorSaid-Houari, Belkacemen
dc.date.accessioned2015-08-03T09:45:23Zen
dc.date.available2015-08-03T09:45:23Zen
dc.date.issued2012-03-07en
dc.identifier.issn00954616en
dc.identifier.doi10.1007/s00245-012-9165-1en
dc.identifier.urihttp://hdl.handle.net/10754/562125en
dc.description.abstractThe goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.en
dc.description.sponsorshipThe first author wishes to thank the Virginia Space Grant Consortium and the Jefferson Scholars Foundation for their support. The second author wants to thank KAUST for its support. Both authors are very grateful to Prof. Irena Lasiecka for many fruitful discussions.en
dc.publisherSpringer Verlagen
dc.subjectBlow upen
dc.subjectDampingen
dc.subjectDynamic boundary conditionen
dc.subjectExponential growthen
dc.subjectFinite timeen
dc.subjectSourceen
dc.subjectWave equationen
dc.titleExistence and asymptotic behavior of the wave equation with dynamic boundary conditionsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalApplied Mathematics and Optimizationen
dc.contributor.institutionDepartment of Mathematics, University of Virginia, Charlottesville, VA 22904, United Statesen
kaust.authorSaid-Houari, Belkacemen
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