On stability and regularity of solutions to generalized Rayleigh-Stokes equations involving delays in Hilbert scales

Nguyen Van Dac; Tran Dinh Ke; Vu Nam Phong

doi:10.3934/eect.2024055

Article Contents

2025, Volume 14, Issue 2: 289-312. Doi: 10.3934/eect.2024055

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On stability and regularity of solutions to generalized Rayleigh-Stokes equations involving delays in Hilbert scales

1.
Faculty of Computer Science and Engineering, Thuyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam
2.
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

^*Corresponding author: Vu Nam Phong
^*Corresponding author: Vu Nam Phong

Received: May 2024

Revised: October 2024

Early access: October 14, 2024

Published online: October 14, 2024

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Abstract

We were concerned with generalized Rayleigh-Stokes equations with nonlinearity involving delays. Our aim was to analyze some sufficient conditions ensuring the existence, stability, and Hölder regularity of solutions under setting in Hilbert scales. This setting allowed us to deal with various cases of the nonlinearity function. Our approach used the resolvent theory, fixed point arguments, and the relation between Hilbert scales and fractional Sobolev spaces.

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Mathematics Subject Classification: Primary: 35B40, 35B65; Secondary: 35C15, 45K05.

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