Abstract
We study the nonlinear wave equation involving the nonlinear damping term ut |ut|m-1 and a source term of type u |u|p-1. For 1 < p ≤ m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data.
| Original language | English |
|---|---|
| Pages (from-to) | 295-308 |
| Number of pages | 14 |
| Journal | Journal of Differential Equations |
| Volume | 109 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1994 Apr 15 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Analysis
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Existence of a solution of the wave equation with nonlinear damping and source terms. / Gueorguiev, Vladimir Simeonov; Todorova, Grozdena.
In: Journal of Differential Equations, Vol. 109, No. 2, 15.04.1994, p. 295-308.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Existence of a solution of the wave equation with nonlinear damping and source terms
AU - Gueorguiev, Vladimir Simeonov
AU - Todorova, Grozdena
PY - 1994/4/15
Y1 - 1994/4/15
N2 - We study the nonlinear wave equation involving the nonlinear damping term ut |ut|m-1 and a source term of type u |u|p-1. For 1 < p ≤ m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data.
AB - We study the nonlinear wave equation involving the nonlinear damping term ut |ut|m-1 and a source term of type u |u|p-1. For 1 < p ≤ m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data.
UR - http://www.scopus.com/inward/record.url?scp=0000028946&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000028946&partnerID=8YFLogxK
U2 - 10.1006/jdeq.1994.1051
DO - 10.1006/jdeq.1994.1051
M3 - Article
AN - SCOPUS:0000028946
VL - 109
SP - 295
EP - 308
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 2
ER -