CUED Publications database

About Blow up of Solutions With Arbitrary Positive Initial Energy to Nonlinear Wave Equations

Bilgin, BA and Kalantarov, VK About Blow up of Solutions With Arbitrary Positive Initial Energy to Nonlinear Wave Equations. (Unpublished)

Full text not available from this repository.

Abstract

We show that blow up of solutions with arbitrary positive initial energy of the Cauchy problem for the abstract wacve eqation of the form $Pu_{tt}+Au=F(u) \ (*)$ in a Hilbert space, where $P,A$ are positive linear operators and $F(\cdot)$ is a continuously differentiable gradient operator can be obtained from the result of H.A. Levine on the growth of solutions of the Cauchy problem for (*). This result is applied to the study of inital boundary value problems for nonlinear Klein-Gordon equations, generalized Boussinesq equations and nonlinear plate equations. A result on blow up of solutions with positive initial energy of the initial boundary value problem for wave equation under nonlinear boundary condition is also obtained.

Item Type: Article
Uncontrolled Keywords: math.AP math.AP
Subjects: UNSPECIFIED
Divisions: Div B > Photonics
Depositing User: Cron Job
Date Deposited: 15 Aug 2017 01:22
Last Modified: 05 Oct 2017 02:06
DOI: