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Regularized solution approximation of a fractional pseudo-parabolic problem with a nonlinear source term and random data

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Listed:
  • Can, Nguyen Huu
  • Zhou, Yong
  • Tuan, Nguyen Huy
  • Thach, Tran Ngoc

Abstract

In this paper, we consider a multi-dimensional fractional pseudo-parabolic problem with nonlinear source in case the input data is measured on a discrete set of points instead of the whole domain. For any number of dimensions, the solution is not stable. This makes the problem we are interested in be ill-posed. Here, we construct regularized solutions for this problem in two cases of number of dimensions (denoted by m) including m=2 and m is arbitrary. In each case, we show the uniqueness of the regularized solution and give the error estimates. Finally, the convergence rate is also investigated numerically.

Suggested Citation

  • Can, Nguyen Huu & Zhou, Yong & Tuan, Nguyen Huy & Thach, Tran Ngoc, 2020. "Regularized solution approximation of a fractional pseudo-parabolic problem with a nonlinear source term and random data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302472
    DOI: 10.1016/j.chaos.2020.109847
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    References listed on IDEAS

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    1. Zhu, Xiaoli & Li, Fuyi & Li, Yuhua, 2018. "Global solutions and blow up solutions to a class of pseudo-parabolic equations with nonlocal term," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 38-51.
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