Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

Do Lan

doi:10.3934/eect.2021002

Article Contents

2022, Volume 11, Issue 1: 259-282. Doi: 10.3934/eect.2021002

This issue Previous Article Existence results for fractional impulsive delay feedback control systems with Caputo fractional derivatives Next Article A canonical model of the one-dimensional dynamical Dirac system with boundary control

Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

Do Lan

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

Published: February 2022

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B40, 35R11, 35C15; Secondary: 45D05, 45K05.

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