Blow up of solutions of the Cauchy problem for a wave equation with nonlinear damping and source terms and positive initial energy

Authors:
Howard A. Levine and Grozdena Todorova

Journal:
Proc. Amer. Math. Soc. **129** (2001), 793-805

MSC (1991):
Primary 35L15, 35Q72

Published electronically:
September 19, 2000

MathSciNet review:
1792187

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

In this paper we consider the long time behavior of solutions of the initial value problem for semi-linear wave equations of the form

Here

We prove that if then for any there are choices of initial data from the energy space with initial energy such that the solution blows up in finite time. If we replace by , where is a sufficiently slowly decreasing function, an analogous result holds.

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Additional Information

**Howard A. Levine**

Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011

Email:
halevine@iastate.edu

**Grozdena Todorova**

Affiliation:
Institute of Mathematics, Bulgarian Academy of Sciences, Boul. Acad. Bonchev bl.8, Sofia 1113, Bulgaria

Address at time of publication:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Email:
grozdena@bas.bg, todorova@math.umm.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05743-9

Received by editor(s):
May 11, 1999

Published electronically:
September 19, 2000

Additional Notes:
The first author was supported in part by NATO grant CRG-95120. The second author was supported by the Institute for Theoretical and Applied Physics at Iowa State University.

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2000
American Mathematical Society