A random regularized approximate solution of the inverse problem for the Burgers' equation
Analysis of PDEs
2017-02-28 v1 Mathematical Physics
math.MP
Probability
Spectral Theory
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.
Cite
@article{arxiv.1702.07987,
title = {A random regularized approximate solution of the inverse problem for the Burgers' equation},
author = {Erkan Nane and Nguyen Hoang Tuan and Nguyen Huy Tuan},
journal= {arXiv preprint arXiv:1702.07987},
year = {2017}
}
Comments
11 pages, submitted for publication