✦ LIBER ✦

Global existence and blow-up of solutions for nonlinear viscoelastic wave equation with degenerate damping and source

✍ Scribed by Xiaosen Han; Mingxin Wang

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 145 KB
Volume: 284
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200810168

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this paper we investigate the global existence and finite time blow‐up of solutions to the nonlinear viscoelastic equation

associated with initial and Dirichlet boundary conditions. Here ∂j denote the sub‐differential of j. Under suitable assumptions on g(·), j(·) and the parameters in the equation, we obtain the global existence of generalized solutions, weak solutions for the equation. The finite time blow‐up of weak solutions for the equation is also established provided the initial energy is negative and the exponent p is greater than the critical value k + m. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

📜 SIMILAR VOLUMES

Blow up and global existence in a nonlin

Blow up and global existence in a nonlinear viscoelastic wave equation

✍ Salim A. Messaoudi 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 133 KB 👁 1 views

## Abstract In this paper the nonlinear viscoelastic wave equation associated with initial and Dirichlet boundary conditions is considered. Under suitable conditions on __g__, it is proved that any weak solution with negative initial energy blows up in finite time if __p__ > __m__. Also the case o

Global existence and nonexistence for a

Global existence and nonexistence for a nonlinear wave equation with damping and source terms

✍ Yong Zhou 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 209 KB

## Abstract In this paper we consider a nonlinear wave equation with damping and source term on the whole space. For linear damping case, we show that the solution blows up in finite time even for vanishing initial energy. The criteria to guarantee blowup of solutions with positive initial energy a

Existence of a Solution of the Wave Equa

Existence of a Solution of the Wave Equation with Nonlinear Damping and Source Terms

✍ V. Georgiev; G. Todorova 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 375 KB

We study the nonlinear wave equation involving the nonlinear damping term \(u_{i}\left|u_{t}\right|^{m-1}\) and a source term of type \(u|u|^{p-1}\). For \(1<p \leqslant m\) we prove a global existence theorem with large initial data. For \(1<m<p\) a blow-up result is established for sufficiently la

Global and Blow-Up Solutions for Nonline

Global and Blow-Up Solutions for Nonlinear Degenerate Parabolic Systems with Crosswise-Diffusion

✍ Zhi-wen Duan; Li Zhou 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 124 KB

Global existence, blow up and asymptotic

Global existence, blow up and asymptotic behaviour of solutions for nonlinear Klein–Gordon equation with dissipative term

✍ Xu Runzhang 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 203 KB

## Abstract We study the Cauchy problem of nonlinear Klein–Gordon equation with dissipative term. By introducing a family of potential wells, we derive the invariant sets and prove the global existence, finite time blow up as well as the asymptotic behaviour of solutions. In particular, we show a s

Global existence and blow-up of the solu

Global existence and blow-up of the solutions for the multidimensional generalized Boussinesq equation

✍ Ying Wang; Chunlai Mu 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 149 KB 👁 1 views

## Abstract In this paper, the existence and the uniqueness of the global solution for the Cauchy problem of the multidimensional generalized Boussinesq equation are obtained. Furthermore, the blow‐up of the solution for the Cauchy problem of the generalized Boussinesq equation is proved. Copyright