... Banach Space and < /b> Nonlinear Partial Differential Equa-tions, vol. 49 of Mathematical Surveys and < /b> Monographs, American Mathematical Society, Provi-dence, RI, USA, 1997.[18] G. Todorova, “Stable and < /b> ... Todorova, “Stable and < /b> unstable sets for the Cauchy problem for a < /b> nonlinear wave equation with < /b> nonlinear damping and < /b> s ource terms,” Journal of Mathematical Analysis and < /b> Applications,vol. 239, no. ... Inequalities and < /b> Applications(1.1 )with< /b> = 0 by making use of the Faedo-Galerkin approximation, and < /b> then consid-ered asymptotic stability of the solution by using Nakao lemma [8]. The background...