Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions

Details Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions

2008-10-06

arxiv.org/abs/0810.1013v1

Advances in Differential Equations 13, 11-12 (2008) 1051-1074

Mathematics

Analysis of PDEs

Scientific paper

In this paper we consider a multi-dimensional damped semiliear wave equation
with dynamic boundary conditions, related to the Kelvin-Voigt damping. We
firstly prove the local existence by using the Faedo-Galerkin approximations
combined with a contraction mapping theorem. Secondly, the exponential growth
of the energy and the $L^p$ norm of the solution is presented.

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