On stability for semilinear generalized Rayleigh-Stokes equation involving delays

Lan, Do; Tuan, Pham

doi:10.1090/qam/1624

Authors: Do Lan and Pham Thanh Tuan
Journal: Quart. Appl. Math. 80 (2022), 701-715
MSC (2020): Primary 35B40, 35R11, 35C15; Secondary 45D05, 45K05
DOI: https://doi.org/10.1090/qam/1624
Published electronically: May 16, 2022
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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 asymptotic behavior of solutions are addressed. By establishing a 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.

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