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

Philip Jameson Graber, Belkacem Said-Houari

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)81-122
Number of pages42
JournalApplied Mathematics & Optimization
Volume66
Issue number1
DOIs
StatePublished - Mar 7 2012

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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