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Global existence and energy decay of solutions to a nonlinear wave equation with a delay term

Global existence and energy decay of solutions to a nonlinear wave equation with a delay term Abstract. We consider the nonlinear wave equation in a bounded domain with a delay term in the internal feedback and prove the global existence of its solutions in Sobolev spaces by means of the energy method combined with the Faedo–Galerkin procedure under a certain condition between the weight of the delay term in the feedback and the weight of the term without delay. Furthermore, we study the asymptotic behavior of solutions using the multiplier method and general weighted integral inequalities. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Global existence and energy decay of solutions to a nonlinear wave equation with a delay term

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References (24)

Publisher
de Gruyter
Copyright
Copyright © 2013 by the
ISSN
1072-947X
eISSN
1572-9176
DOI
10.1515/gmj-2013-0006
Publisher site
See Article on Publisher Site

Abstract

Abstract. We consider the nonlinear wave equation in a bounded domain with a delay term in the internal feedback and prove the global existence of its solutions in Sobolev spaces by means of the energy method combined with the Faedo–Galerkin procedure under a certain condition between the weight of the delay term in the feedback and the weight of the term without delay. Furthermore, we study the asymptotic behavior of solutions using the multiplier method and general weighted integral inequalities.

Journal

Georgian Mathematical Journalde Gruyter

Published: Mar 1, 2013

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