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

作者：Nane Erkan; Nguyen Hoang Tuan^*; Nguyen Huy Tuan^*

来源：Statistics & Probability Letters, 2018, 132: 46-54.

DOI：10.1016/j.spl.2017.08.014

• Inverse problem
• Burgers equation
• Random approximation

In this paper, we find a regularized approximate solution for an inverse problem for Burgers' equation. The solution of the inverse problem for 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.

• 出版日期2018-1