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Decay Results for a Viscoelastic Problem with Nonlinear Boundary Feedback and Logarithmic Source Term.
- Source :
- Journal of Dynamical & Control Systems; Jan2022, Vol. 28 Issue 1, p71-89, 19p
- Publication Year :
- 2022
-
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 ′ (t) ≤ − ξ (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) = s<superscript>p</superscript> 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- NONLINEAR equations
POTENTIAL well
CONVEX functions
GAUSSIAN channels
Subjects
Details
- Language :
- English
- ISSN :
- 10792724
- Volume :
- 28
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Dynamical & Control Systems
- Publication Type :
- Academic Journal
- Accession number :
- 154535645
- Full Text :
- https://doi.org/10.1007/s10883-020-09522-1