Logarithmic decay of wave equations with Cauchy-Ventcel boundary conditions
FU Xiao-yu
LIU Xu
ZHU Xian-zheng
Abstract：This paper is devoted to a study of decay properties for a class of wave equations with Cauchy-Ventcel boundary conditions and a local internal damping. Based on an estimate on the resolvent operator, solutions of the wave equations under consideration are proved to decay logarithmically without any geometric control condition. The proof of the decay result relies on the interpolation inequalities for an elliptic equation with Cauchy-Ventcel boundary conditions and the estimate of the resolvent operator for that equation. The main tool to derive the desired interpolation inequality is global Carleman estimate.
Keywords：Logarithmic decaywave equationsCauchy-Ventcel boundary conditionCarleman estimate
Publication Date：2019-11-28
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：7( 1879-1885 )