American Institute of Mathematical Sciences

doi: 10.3934/eect.2021002
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Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

 Faculty of Computer Science and Engineering, Thuyloi University, 175 Tay Son, Dong Da, Hanoi, 100000, Vietnam

Received  June 2020 Revised  October 2020 Early access January 2021

Fund Project: This research is funded by Thuyloi University Foundation for Science and Technology under grant number TLU.STF.19-04

We study the generalized Rayleigh-Stokes problem involving a fractional derivative and nonlinear perturbation. Our aim is to analyze some sufficient conditions ensuring the global solvability, regularity and asymptotic stability of solutions. In particular, if the nonlinearity is Lipschitzian then the mild solution of the mentioned problem becomes a classical one and its convergence to equilibrium point is proved.

Citation: Do Lan. Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations. Evolution Equations & Control Theory, doi: 10.3934/eect.2021002
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