Approximation of mild solutions of a semilinear fractional differential equation with random noise

Nguyen Huy Tuan; Erkan Nane; Donal O'Regan; Nguyen Duc Phuong

doi:10.1090/proc/15029

Approximation of mild solutions of a semilinear fractional differential equation with random noise

Nguyen Huy Tuan
, Erkan Nane
, Donal O'Regan
, Nguyen Duc Phuong

Mathematics

Ton Duc Thang University
Auburn University
University of Science Ho Chi Minh City

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

9 Citations (Scopus)

Abstract

We study for the ﬁrst time the Cauchy problem for semilinear fractional elliptic equations with random data. This paper is concerned with the Gaussian white noise model for initial Cauchy data. We establish the ill-posedness of the problem. Then we propose the Fourier truncation method for stabilizing the ill-posed problem. Some convergence rates between the exact solution and the regularized solution is established in L² and H^q norms.

Original language	English
Pages (from-to)	3339-3357
Number of pages	19
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	8
DOIs	https://doi.org/10.1090/proc/15029
Publication status	Published - Aug 2020

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abstract = "We study for the ﬁrst time the Cauchy problem for semilinear fractional elliptic equations with random data. This paper is concerned with the Gaussian white noise model for initial Cauchy data. We establish the ill-posedness of the problem. Then we propose the Fourier truncation method for stabilizing the ill-posed problem. Some convergence rates between the exact solution and the regularized solution is established in L2 and Hq norms.",

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AU - O'Regan, Donal

AU - Phuong, Nguyen Duc

PY - 2020/8

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AB - We study for the ﬁrst time the Cauchy problem for semilinear fractional elliptic equations with random data. This paper is concerned with the Gaussian white noise model for initial Cauchy data. We establish the ill-posedness of the problem. Then we propose the Fourier truncation method for stabilizing the ill-posed problem. Some convergence rates between the exact solution and the regularized solution is established in L2 and Hq norms.

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JF - Proceedings of the American Mathematical Society

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Approximation of mild solutions of a semilinear fractional differential equation with random noise

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