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2026, Volume 11, Issue 8: 24691-24716. doi: 10.3934/math.2026994
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Research article

Long-time dynamics of a fractional viscoelastic equation with infinite memory

  • College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
  • Published: 12 August 2026

  • MSC : 35R11, 35A01, 35B30, 35B41, 37N15

  • This work was concerned with a fractional viscoelastic equation with infinite memory. We first proved the global well-posedness of solutions in a suitable function space. Moreover, we derived a stabilizability estimate by using the perturbed energy method. Then, by utilizing the quasi-stability of the corresponding gradient dynamical system, we found the existence of global attractors with finite fractal dimension.

    Citation: Junfeng Li, Yang Liu, Qiong Li, Xu Yan. Long-time dynamics of a fractional viscoelastic equation with infinite memory[J]. AIMS Mathematics, 2026, 11(8): 24691-24716. doi: 10.3934/math.2026994

    Related Papers:

  • This work was concerned with a fractional viscoelastic equation with infinite memory. We first proved the global well-posedness of solutions in a suitable function space. Moreover, we derived a stabilizability estimate by using the perturbed energy method. Then, by utilizing the quasi-stability of the corresponding gradient dynamical system, we found the existence of global attractors with finite fractal dimension.



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