A new stability results for the backward heat equation

TL;DR

This paper introduces a regularization approach for the nonlinear inverse heat problem in unbounded regions, providing new convergence rates, sharp error estimates, and optimal convergence results at t=0.

Contribution

It extends existing results by applying Fourier methods to regularize the nonlinear inverse heat problem and establishes new convergence and error estimates.

Findings

New convergence rates for the regularized solution

Sharp error estimates between approximate and exact solutions

Proof of optimal convergence at t=0

Abstract

In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. Especially, the optimal convergence of the approximate solution at t = 0 is also proved. This work extends to many earlier results in (f2,f3, hao1,Quan,tau1, tau2, Trong3,x1).