Abstract
The main goal of this work is to investigate the long-time behavior of a viscoelastic equation with a logarithmic source term and a nonlinear feedback localized on a part of the boundary. In the framework of potential well, we first show the global existence. Then, we discuss the asymptotic behavior of the problem with a very general assumption on the behavior of the relaxation function g, namely, $g^{\prime }(t)\le -\xi (t) G(g(t))$ . We establish explicit and general decay results from which we can recover the well-known exponential and polynomial rates when G(s) = sp and p covers the full admissible range [1,2). Our results are obtained without imposing any restrictive growth assumption on the boundary damping term. This work generalizes and improves many earlier results in the literature.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
