The aim of the paper is to study wave equation in a bounded open subset of the euclidean space in dimension greater or equal than two, with an hyperbolic dynamical boundary condition involving the Laplace Beltrami operator. Moreover the problem will include internal and boundary damping terms as well as internal and boudary sources. Local well-posedness of the problem is studied, as well as regularity of solutions. Moreover a blow-up and a global existence result are given, under different assumptions on the nonlinearities involved.
ON THE WAVE EQUATION WITH HYPERBOLIC DYNAMICAL BOUNDARY CONDITIONS, INTERIOR AND BOUNDARY DAMPING AND SOURCE
VITILLARO, Enzo
2017
Abstract
The aim of the paper is to study wave equation in a bounded open subset of the euclidean space in dimension greater or equal than two, with an hyperbolic dynamical boundary condition involving the Laplace Beltrami operator. Moreover the problem will include internal and boundary damping terms as well as internal and boudary sources. Local well-posedness of the problem is studied, as well as regularity of solutions. Moreover a blow-up and a global existence result are given, under different assumptions on the nonlinearities involved.File in questo prodotto:
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