On coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term
type: Item
instance of: scholarly article
title: On coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term
zbMATH Open document ID: 1032.35139
DOI: 10.1016/S0096-3003(01)00031-5
author: Jeong Ja Bae
author: Jong Yeoul Park
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The system of two Kirchhoff equations with a strong damping is considered in a cylindrical domain. On one part of the lateral surface of the cylinder, \(\Gamma_1 , \) both solutions and normal derivatives are zero and on the rest of the surface, \(\Gamma_0 , \) expressions containing damping and memory terms are given. The authors claim existence of global solutions and the decay of the energy of the system. Set up of two conditions (1.3) for the each equation on \(\Gamma_1, \) makes the problem to look like overdetermined. Besides, in the existence part of the paper it was not proved that the normal derivatives of solutions on \(\Gamma_1 \) are zero.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 74H20
Mathematics Subject Classification ID: 74H40
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 1861083
zbMATH Keywords: Kirchhoff equation
zbMATH Keywords: existence
zbMATH Keywords: stability
zbMATH Keywords: strong damping
zbMATH Keywords: cylindrical domain
MaRDI profile type: Publication
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full work available at URL: s0096-3003(01)00031-5
OpenAlex ID: W2077438734
description: scientific article; zbMATH DE number 1861083