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Nguyen Huy Tuan1, Dang Duc Trong2 (2009). A new regularized method for two dimensional nonhomogeneous backward heat problem. Applied Mathematics and Computation, Volume 215, Issue 3, pp, 873-880.

 1Department of Mathematics and Informatics, Ton Duc Thang University, 98, Ngo Tat To, Binh Thanh district, Ho Chi Minh City, VietNam.
2Department of Mathematics, HoChiMinh City National University, 227 Nguyen Van Cu, Q. 5, HoChiMinh City, VietNam.

Abstract. We consider the problem of finding, from the final data u(x,y,T)=g(x,y), the initial data u(x,y,0) of the temperature function u(x,y,t),(x,y)ÎI=(0,π)×(0,π),tÎ [0,T] satisfying the following system

The problem is severely ill-posed. In this paper a simple and convenient new regularization method for solving this problem is considered. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively.