EXISTENCE OF A SOLUTION OF THE WAVE-EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS

Authors
GEORGIEV V TODOROVA G
Citation
V. Georgiev et G. Todorova, EXISTENCE OF A SOLUTION OF THE WAVE-EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS, Journal of differential equations, 109(2), 1994, pp. 295-308
Citations number
12
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Journal of differential equations → ACNP
ISSN journal
00220396
Volume
109
Issue
2
Year of publication
1994
Pages
295 - 308
Database
ISI
SICI code
0022-0396(1994)109:2<295:EOASOT>2.0.ZU;2-D
Abstract
We study the nonlinear wave equation involving the nonlinear damping t erm u(t)\u(t)\m-1 and a source term of type u\u\p-1. For 1 < p less-th an-or-equal-to m we prove a global existence theorem with large initia l data. For 1 < m < p a blow-up result is established for sufficiently large initial data. (C) 1994 Academic Press, Inc.