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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.
Georgian Mathematical Journal – de Gruyter
Published: Mar 1, 2013
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