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

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

Chaos, Solitons & Fractals, 2021, vol. 145, issue C

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.

Keywords: Pseudo-parabolic equation; Non-local; Fractional Laplacian; Gaussian white noise; Random noise; Regularized solution; Ill-posed (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001235

DOI: 10.1016/j.chaos.2021.110771

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