On stability for semilinear generalized Rayleigh-Stokes equation involving delays
Abstract
We consider a functional semilinear Rayleigh-Stokes equation involving fractional derivative. Our aim is to analyze some circumstances, in those the global solvability and some results on asymptotic behavior of solutions take place. By establishing a new Halanay type inequality, we show the dissipativity and asymptotic stability of solutions to our problem. In addition, we prove the existence of a compact set of decay solutions by using local estimates and fixed point arguments.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2020
- DOI:
- 10.48550/arXiv.2011.00545
- arXiv:
- arXiv:2011.00545
- Bibcode:
- 2020arXiv201100545T
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35B40;
- 35R11;
- 35C15;
- 45D05;
- 45K05