Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T03:23:05.681Z Has data issue: false hasContentIssue false

Blow-up for the wave equation with nonlinear source and boundary damping terms

Published online by Cambridge University Press:  20 July 2015

Alessio Fiscella
Affiliation:
Dipartimento di Matematica ‘Federigo Enriques’, Università di Milano, Via Cesare Saldini 50, 20133 Milano, Italy, ([email protected])
Enzo Vitillaro
Affiliation:
Dipartimento di Matematica ed Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy, ([email protected])

Abstract

The paper deals with blow-up for the solutions of an evolution problem consisting in a semilinear wave equation posed in a bounded C1,1 open subset of ℝn, supplied with a Neumann boundary condition involving a nonlinear dissipation. The typical problem studied is

where ∂Ω = Γ0Γ1, Γ0Γ1 = ∅, σ(Γ0) > 0, 2 < p ≤ 2(n − 1)/(n − 2) (when n ≥ 3), m > 1, αL(Γ1), α ≥ 0 and β ≥ 0. The initial data are posed in the energy space.The aim of the paper is to improve previous blow-up results concerning the problem.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)