Global nonexistence of solutions for viscoelastic wave equations of Kirchhoff type with high energy
type: Item
instance of: scholarly article
title: Global nonexistence of solutions for viscoelastic wave equations of Kirchhoff type with high energy
zbMATH Open document ID: 1242.35176
DOI: 10.1155/2012/530861
author: Linghui Hong
author: Wenjun Liu
author: Gang Li
published in: Journal of Function Spaces and Applications
publication date: 2012-05-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.5916
review text: Summary: We consider viscoelastic wave equations of the Kirchhoff type \[ u_{tt} - M(||\nabla u||^2_2) \Delta u + \int^t_0 g(t - s) \Delta u(s)ds + u_t = |u|^{p-1}u \] with Dirichlet boundary conditions, where \(||\cdot||_p\) denotes the norm in the Lebesgue space \(L^p\). Under some suitable assumptions on \(g\) and the initial data, we establish a global nonexistence result for certain solutions with arbitrarily high energy, in the sense that \[ \lim_{t \rightarrow T^{\ast -}} (||u(t)||^2_2 + \int^t_0 ||u(s)||^2_2 ds) = \infty \] for some \(0 < T^\ast < +\infty\).
Mathematics Subject Classification ID: 35L72
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35R09
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 6032365
zbMATH Keywords: Dirichlet boundary conditions
MaRDI profile type: Publication
OpenAlex ID: W2168085895
Wikidata QID: Q58908303
arXiv ID: 1109.5916
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description: scientific article; zbMATH DE number 6032365