Results 11 to 20 of about 8,522 (253)
Inverse Estimates for Nonhomogeneous Backward Heat Problems [PDF]
Journal of Applied Mathematics, 2014 We investigate the inverse problem in the nonhomogeneous heat equation involving the recovery of the initial temperature from measurements of the final temperature. This problem is known as the backward heat problem and is severely ill-posed.
Tao Min, Weimin Fu, Qiang Huang
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Error estimates of a difference approximation method for a backward heat conduction problem [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 We introduce a central difference method for a backward heat conduction problem (BHCP). Error estimates for this method are provided together with a selection rule for the regularization parameter (the space step length).
Xiang-Tuan Xiong +3 more
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A nonhomogeneous backward heat problem: Regularization and error estimates
Electronic Journal of Differential Equations, 2008 We consider the problem of finding the initial temperature, from the final temperature, in the nonhomogeneous heat equation $$displaylines{ u_t-u_{xx}= f(x,t),quad (x,t)in (0,pi)imes (0,T),\ u(0,t)= u(pi,t)= 0, quad (x,t) in (0,pi)imes(0,T ...
Trong Dang Duc, Huy Tuan Nguyen
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A Discretized Tikhonov Regularization Method for a Fractional Backward Heat Conduction Problem [PDF]
Abstract and Applied Analysis, 2014 We propose a numerical reconstruction method for solving a time-fractional backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered ...
Zhi-Liang Deng, Xiao-Mei Yang
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Regularization and error estimates for nonhomogeneous backward heat problems
Electronic Journal of Differential Equations, 2006 In this article, we study the inverse time problem for the non-homogeneous heat equation which is a severely ill-posed problem. We regularize this problem using the quasi-reversibility method and then obtain error estimates on the approximate ...
Duc Trong Dang, Huy Tuan Nguyen
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A wavelet method for solving backward heat conduction problems
Electronic Journal of Differential Equations, 2017 In this article, we consider the backward heat conduction problem (BHCP). This classical problem is more severely ill-posed than some other problems, since the error of the data will be exponentially amplified at high frequency components.
Chunyu Qiu, Xiaoli Feng
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Regularization of the backward stochastic heat conduction problem [PDF]
Journal of Inverse and Ill-posed Problems, 2021 Abstract In this paper, we study the backward problem for the stochastic parabolic heat equation driven by a Wiener process. We show that the problem is ill-posed by violating the continuous dependence on the input data. In order to restore stability, we apply a filter regularization method which is completely new in the stochastic ...
Huy Tuan, N +3 more
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A new regularization for time-fractional backward heat conduction problem
Journal of Inverse and Ill-posed Problems, 2023 Abstract It is well known that the backward heat conduction problem of recovering the temperature u ( ⋅
M. Thamban Nair, P. Danumjaya
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Stochastic convergence of regularized solutions for backward heat conduction problems
CoRR, 2023 In this paper, we study the stochastic convergence of regularized solutions for backward heat conduction problems. These problems are recognized as ill-posed due to the exponential decay of eigenvalues associated with the forward problems. We derive an error estimate for the least-squares regularized minimization problem within the framework of ...
Zhongjian Wang +2 more
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On the backward heat problem: evaluation of the norm of [PDF]
International Journal of Mathematics and Mathematical Sciences, 1980 We show in this paper that ‖Δu‖ = ‖ut‖ is bounded ∀t ≤ T(0) < T if one imposes on u (solution of the backward heat equation) the condition ‖u(x, t)‖ ≤ M. A Hölder type of inequality is also given if one supposes ‖ut(x, T)‖ ≤ K.
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