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Alain Pham Ngoc Dinh1, Dang Duc Trong2, Pham Hoang Quan3, Nguyen Huy Tuan4 (2009). A new stability results for the backward heat equation. 13 pages.

1MAPMO, UMR CNRS 6628, Orleans University, France.
2Department of Mathematics ,HoChiMinh City National University, 227 Nguyen Van Cu, Q. 5, HoChiMinh City, VietNam.
3Department of Mathematics, Sai Gon University, Ho Chi Minh city, Viet Nam.
4Department of Mathematics and Informatics,Ton Duc Thang University, 98 Ngo Tat To, Binh Thanh district, Ho Chi Minh city , Viet Nam.

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 pro- vided. Especially, the optimal convergence of the approximate solution at t = 0 is also proved. This work extends to many earlier results in [7, 8, 10, 15, 17, 18, 21, 24].