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The Truncation Method for a Two-Dimensional Nonhomogeneous Backward Heat Problem
Applied Mathematics and Computation, 2010The backward heat problem with homogeneous Dirichlet condition on the rectangle is considered. The problem is severely ill-posed. Using the truncation method for Fourier series a simple regularized solution is proposed which not only works on a very weak condition on the exact data but also attains, due to the smoothness of the exact solution, explicit
Phan Thành Nam, Tuan Nguyen Huy
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Regularization of backward heat conduction problem
Communications in Nonlinear Science and Numerical Simulation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rashidinia, Jalil, Azarnavid, Babak
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Group Preserving Scheme for Backward Heat Conduction Problems
International Journal of Heat and Mass Transfer, 2004Inverse one-dimensional transient heat conduction problem is considered. Known are the Dirichlet boundary conditions and final time. The initial conditions are sought for. The algorithm starts with a transformation \(s=T-t\) to invert the arrow of time.
Chein-Shan Liu
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The Method of Fundamental Solutions for the Backward Heat Conduction Problem
Inverse Problems in Science and Engineering, 2005In this article a meshless numerical scheme for solving the backward heat conduction problem (BHCP) is proposed. The numerical solution is developed by using the fundamental solution of the heat equation as a basis function. The standard Tikhonov regularization technique and the L-curve method are adopted for solving the resultant ill-conditioned ...
N S Mera
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On a Backward Heat Conduction Problem Associated with Asymmetric Final Data
Acta Mathematica Vietnamica, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Le Minh Triet +2 more
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On a Backward Heat Problem With Time-Dependent Coefficient: Regularization and Error Estimates
Applied Mathematics and Computation, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tuan Nguyen Huy
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Regularization Technique for an Inverse Space-Fractional Backward Heat Conduction Problem
Journal of Scientific Computing, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Milad Karimi +2 more
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A modified integral equation method of the semilinear backward heat problem
Applied Mathematics and Computation, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nguyen Huy Tuan +2 more
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Optimal control problem for the backward heat equation
Siberian Mathematical Journal, 1993The optimal control problem of minimizing a quadratic functional for the system described by the Cauchy problem for the backward heat equation in which the control appears in boundary conditions is investigated. Under suitable conditions the existence and uniqueness of the optimal solution is proved.
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DeepBHCP: Deep neural network algorithm for solving backward heat conduction problems
Computer Physics Communications, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Farinaz Mostajeran, Reza Mokhtari
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