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Long time behavior of solutions for time-fractional pseudo-parabolic equations involving time-varying delays and superlinear nonlinearities

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Abstract

We study the long time behavior of solutions for time-fractional pseudo-parabolic equations involving time-varying delays and nonlinear pertubations, where the nonlinear term is allowed to have superlinear growth. Concerning the associated linear problem, we establish a variation-of-parameters formula of mild solutions and prove some regularity estimates of resolvent operators. In addition, thanks to local estimates on Hilbert scales, fixed point arguments and a new Halanay type inequality, we obtain some results on the global solvability, stability, dissipativity and the existence of decay solutions to our problem.

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Authors and Affiliations

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

    Do Lan

  2. Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam

    Tran Van Tuan

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  1. Do Lan
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  2. Tran Van Tuan
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DL and TVT wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Do Lan.

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Lan, D., Van Tuan, T. Long time behavior of solutions for time-fractional pseudo-parabolic equations involving time-varying delays and superlinear nonlinearities. J. Pseudo-Differ. Oper. Appl. 14, 74 (2023). https://doi.org/10.1007/s11868-023-00569-9

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  • DOI: https://doi.org/10.1007/s11868-023-00569-9

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