A new regularized method for two dimensional nonhomogeneous backward heat problem |
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| Authors: | Nguyen Huy Tuan Dang Duc Trong |
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| Institution: | aDepartment of Mathematics and Informatics, Ton Duc Thang University, 98, Ngo Tat To, Binh Thanh district, Ho Chi Minh City, Viet nam;bDepartment of Mathematics, HoChiMinh City National University, 227 Nguyen Van Cu, Q. 5, HoChiMinh City, Viet nam |
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| 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) I=(0,π)×(0,π),t0,T] satisfying the following systemThe 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. |
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| Keywords: | Backward heat problem Ill-posed problem Nonhomogeneous heat Contraction principle |
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