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arXiv · 1702.07987

A random regularized approximate solution of the inverse problem for the Burgers' equation

Erkan Nane·Nguyen Hoang Tuan·Nguyen Huy Tuan
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Abstract

In this paper, we find a regularized approximate solution for an inverse problem for the Burgers' equation. The solution of the inverse problem for the Burgers' equation is ill-posed, i.e., the solution does not depend continuously on the data. The approximate solution is the solution of a regularized equation with randomly perturbed coefficients and randomly perturbed final value and source functions. To find the regularized solution, we use the modified quasi-reversibility method associated with the truncated expansion method with nonparametric regression. We also investigate the convergence rate.

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Erkan Nane, Nguyen Hoang Tuan, Nguyen Huy Tuan. 2017-02-26. A random regularized approximate solution of the inverse problem for the Burgers' equation. https://arxiv.org/abs/1702.07987

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