A new stability results for the backward heat equation

Alain Pham Ngoc Dinh (1) , Dang Duc Trong (2) , Pham Hoang Quan (2, 3) , Nguyen Huy Tuan (4)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 UNS-HCMC - University of Natural Sciences- HoChiMinh City
3 Mathematics department
4 Department of Mathematics and Informatics

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).

Mots clés: Backward heat problem; Ill-posed problem; Fourier Transform; Contraction principle.; Contraction principle

Domaines: Equations aux dérivées partielles [math.AP]

Alain Pham Ngoc Dinh, Dang Duc Trong, Pham Hoang Quan, Nguyen Huy Tuan. A new stability results for the backward heat equation. 2009. ⟨hal-00431878⟩