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On a pseudo-parabolic equations with a non-local term of the Kirchhoff type with random Gaussian white noise

Author

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  • Phuong, Nguyen Duc
  • Tuan, Nguyen Huy
  • Hammouch, Zakia
  • Sakthivel, Rathinasamy

Abstract

This paper is concerned with a solution of backward pseudo-Parabolic equationut−αΔut+G(∥∇u∥L2(Ω))(−Δ)βu=K(t,x)subject to the final data which is blurred by random Gaussian white noise. The primary aim of this work is to obtain the solution u. This problem is severely ill-posed (the solution’s behavior does not change continuously with the final condition). By using a statistical method, we estimate the value data from observation data and the Fourier truncation method is used to propose a regularized solution. Under some priori assumptions, we derive an error estimate between a mild solution and its regularized solution. Finally, a numerical example is given to illuminate the effect of our method.

Suggested Citation

  • Phuong, Nguyen Duc & Tuan, Nguyen Huy & Hammouch, Zakia & Sakthivel, Rathinasamy, 2021. "On a pseudo-parabolic equations with a non-local term of the Kirchhoff type with random Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001235
    DOI: 10.1016/j.chaos.2021.110771
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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.
    2. Joan Castillo, 1994. "The singly truncated normal distribution: A non-steep exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 57-66, March.
    3. Tuan, Nguyen Huy & Baleanu, Dumitru & Thach, Tran Ngoc & O’Regan, Donal & Can, Nguyen Huu, 2020. "Approximate solution for a 2-D fractional differential equation with discrete random noise," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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    Cited by:

    1. Djennadi, Smina & Shawagfeh, Nabil & Abu Arqub, Omar, 2021. "A fractional Tikhonov regularization method for an inverse backward and source problems in the time-space fractional diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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