CAUCHY-PROBLEM FOR A NONLINEAR-WAVE EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS

Authors
TODOROVA G
Citation
G. Todorova, CAUCHY-PROBLEM FOR A NONLINEAR-WAVE EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 326(2), 1998, pp. 191-196
Citations number
11
Categorie Soggetti
Mathematics,Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
326
Issue
2
Year of publication
1998
Pages
191 - 196
Database
ISI
SICI code
0764-4442(1998)326:2<191:CFANEW>2.0.ZU;2-6
Abstract
We study the Cauchy problem for the nonlinear wave equation with nonli near damping au(t)\u(t)\(m-1) and a nonlinear source term of type bu\u \(p-1). When 1 < p less than or equal to m, a global existence result is established for any initial data. When 1 < m < p, a finite time blo w-up result is proved for compactly supported data with negative initi al energy.