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dc.contributor.authorGraber, Philip Jameson
dc.contributor.authorSaid-Houari, Belkacem
dc.date.accessioned2015-08-03T09:45:23Z
dc.date.available2015-08-03T09:45:23Z
dc.date.issued2012-03-07
dc.identifier.issn00954616
dc.identifier.doi10.1007/s00245-012-9165-1
dc.identifier.urihttp://hdl.handle.net/10754/562125
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.
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.
dc.publisherSpringer Nature
dc.subjectBlow up
dc.subjectDamping
dc.subjectDynamic boundary condition
dc.subjectExponential growth
dc.subjectFinite time
dc.subjectSource
dc.subjectWave equation
dc.titleExistence and asymptotic behavior of the wave equation with dynamic boundary conditions
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalApplied Mathematics & Optimization
dc.contributor.institutionDepartment of Mathematics, University of Virginia, Charlottesville, VA 22904, United States
kaust.personSaid-Houari, Belkacem


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