Blow up in solutions of a linear wave equation with mixed nonlinear boundary conditions

Authors
Messaoudi, SA
Citation
Sa. Messaoudi, Blow up in solutions of a linear wave equation with mixed nonlinear boundary conditions, AR J SCI EN, 25(1A), 2000, pp. 39-44
Citations number
15
Categorie Soggetti
Engineering Management /General
Journal title
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
ISSN journal
03779211 → ACNP
Volume
25
Issue
1A
Year of publication
2000
Pages
39 - 44
Database
ISI
SICI code
0377-9211(200001)25:1A<39:BUISOA>2.0.ZU;2-4
Abstract
We consider a one-dimensional linear wave equation associated with mixed no nlinear boundary conditions. We prove a local existence result and we then show that the nonlinearity at the boundary causes a finite time blow up of the solution, even for small and smooth initial data.