𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Blowup of solutions for a class of non-linear evolution equations with non-linear damping and source terms

✍ Scribed by Yang Zhijian

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
96 KB
Volume
25
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We consider the blowup of solutions of the initial boundary value problem for a class of non‐linear evolution equations with non‐linear damping and source terms. By using the energy compensation method, we prove that when p>max{m, α}, where m, α and p are non‐negative real numbers and m+1, α+1, p+1 are, respectively, the growth orders of the non‐linear strain terms, damping term and source term, under the appropriate conditions, any weak solution of the above‐mentioned problem blows up in finite time. Comparison of the results with the previous ones shows that there exist some clear condition boundaries similar to thresholds among the growth orders of the non‐linear terms, the states of the initial energy and the existence and non‐existence of global weak solutions. Copyright © 2002 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

Existence and asymptotic behaviour of so
Existence and asymptotic behaviour of solutions for a class of quasi-linear evolution equations with non-linear damping and source terms
✍ Yang Zhijian 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 170 KB 👁 1 views

## Abstract We consider a class of quasi‐linear evolution equations with non‐linear damping and source terms arising from the models of non‐linear viscoelasticity. By a Galerkin approximation scheme combined with the potential well method we prove that when __m__<__p__, where __m__(⩾0) and __p__ ar

Global non-existence of solutions of a c
Global non-existence of solutions of a class of wave equations with non-linear damping and source terms
✍ Salim A. Messaoudi; Belkacem Said Houari 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 98 KB 👁 1 views

## Abstract In this paper we consider the non‐linear wave equation __a,b__>0, associated with initial and Dirichlet boundary conditions. We prove, under suitable conditions on __α,β,m,p__ and for negative initial energy, a global non‐existence theorem. This improves a result by Yang (__Math. Meth

On the decay of solutions for a class of
On the decay of solutions for a class of quasilinear hyperbolic equations with non-linear damping and source terms
✍ Salim A. Messaoudi 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 104 KB 👁 1 views

## Abstract In this paper, we consider the non‐linear wave equation __a__,__b__>0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on __α__, __m__, and __p__, we give precise decay rates for the solution. In particular, we show that for __m__=0, the decay is ex

Existence and non-existence of global so
Existence and non-existence of global solutions for a class of non-linear wave equations
✍ Chen Guowang; Yang Zhijian 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 135 KB 👁 2 views

This paper studies the existence and the non-existence of global solutions to the initial boundary value problems for the non-linear wave equation The paper proves that every above-mentioned problem has a unique global solution under rather mild con"ning conditions, and arrives at some su$cient con

Initial boundary value problem for a cla
Initial boundary value problem for a class of non-linear strongly damped wave equations
✍ Yang Zhijian 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 182 KB 👁 1 views

## Abstract The paper studies the existence, asymptotic behaviour and stability of global solutions to the initial boundary value problem for a class of strongly damped non‐linear wave equations. By a H00.5ptk‐Galerkin approximation scheme, it proves that the above‐mentioned problem admits a unique