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A backward parabolic equation with a time-dependent coefficient: Regularization and error estimates
Authors:Triet Minh Le  Quan Hoang Pham  Trong Duc Dang  Tuan Huy Nguyen
Institution:1. Department of Mathematics and Applications, SaiGon University, 273 An Duong Vuong, Dist. 5, Ho Chi Minh City, Viet Nam;2. Department of Mathematics, University of Natural Science, Vietnam National University, 227 Nguyen Van Cu, Dist.5, Ho Chi Minh City, Viet Nam;3. Department of Science and Technology, Hoa Sen University, 8 Nguyen Van Trang, Dist. 1, Ho Chi Minh City, Viet Nam
Abstract:We consider the problem of determining the temperature u(x,t)u(x,t), for (x,t)∈0,π]×0,T)(x,t)0,π]×0,T) in the parabolic equation with a time-dependent coefficient. This problem is severely ill-posed, i.e., the solution (if it exists) does not depend continuously on the given data. In this paper, we use a modified method for regularizing the problem and derive an optimal stability estimation. A numerical experiment is presented for illustrating the estimate.
Keywords:35K05  35K99  47J06  47H10
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