Existence, asymptotic behaviour, and blow up of solutions for a class of nonlinear wave equations with dissipative and dispersive terms
Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, vol.64, no.5-6, pp.315-326, 2009 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 64 Issue: 5-6
- Publication Date: 2009
- Doi Number: 10.1515/zna-2009-5-605
- Journal Name: Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.315-326
- Keywords: Asymptotic behaviour, Blow up of solutions, Global solution, Initial boundary value problem, Nonlinear wave equation
- Open Archive Collection: AVESIS Open Access Collection
- İstanbul Ticaret University Affiliated: Yes
Abstract
We consider the existence, both locally and globally in time, the asymptotic behaviour, and the blow up of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative and dispersive terms. Under rather mild conditions on the nonlinear term and the initial data we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the solution decays exponentially to zero as t → +∞. Finally, under a suitable condition on the nonlinear term, we prove that the local solutions with negative and nonnegative initial energy blow up in finite time. © 2009 Verlag der Zeitschrift für Naturforschung, Tübingen.