On internal elastic membrane with strong damping.
type: Item
instance of: scholarly article
title: On internal elastic membrane with strong damping.
zbMATH Open document ID: 1249.35217
author: O. A. Lima
author: Fágner D. Araruna
author: M. R. Clark
published in: Differential and Integral Equations
publication date: 2012-05-11T00:00:00Z
review text: Under some assumptions on \(M,A,F\) the authors prove existence and uniqueness of weak and strong solutions of the initial problem to the equation \(u_{tt}+M(\| u(t)\| ^2)Au(t)+Fu(t)+Au'(t)=0\) in a real Hilbert space, where \(t\in (0,T)\), \(M\) is degenerate real function and \(A,F\) are operators. Furthermore, energy decay \(E(t)\leq C(1+t)^{-(1+1/s)}\) of the initial Dirichlet boundary value problem to the equation \(u_{tt}-\| u(t)\| ^{2s}\Delta u+g(u)-\Delta u_t=0\) is established.
reviewed by: Marie Kopáčková
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 6033864
zbMATH Keywords: Kirchhoff model
zbMATH Keywords: strong damping
zbMATH Keywords: asymptotic decay
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6033864