ON TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATION WITH A LOCALIZED NONLINEAR DISSIPATION IN BOUNDED DOMAIN

doi:10.1016/S0252-9602(12)60068-X

Abstract

Abstract:

In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi-cally different types of materials, one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary, while the other is a Kirchhoff type wave equation with nonlinear memory.

Key words: Existence of solution, uniform decay, transmission problem, Kirchhoff type wave equation, boundary value problem, localized dissipation

CLC Number:

35L05

Jeong Ja Bae. ON TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATION WITH A LOCALIZED NONLINEAR DISSIPATION IN BOUNDED DOMAIN[J].Acta mathematica scientia,Series B, 2012, 32(3): 893-906.

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ON TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATION WITH A LOCALIZED NONLINEAR DISSIPATION IN BOUNDED DOMAIN

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