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Regularization of the backward heat equation via heatlets [PDF]
Electronic Journal of Differential Equations, 2008 Shen and Strang [16] introduced heatlets in order to solve the heat equation using wavelet expansions of the initial data. The advantage of this approach is that heatlets, or the heat evolution of the wavelet basis functions, can be easily computed ...
Emily McNabb +2 more
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A Galerkin method for the forward-backward heat equation [PDF]
Mathematics of Computation, 1991 In this paper a new variational method is proposed for the numerical approximation of the solution of the forward-backward heat equation. The approach consists of first reducing the second-order problem to an equivalent first-order system, and then using
J.-L. Liu, A. K. Aziz
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Wick product and backward heat equation
Mediterranean Journal of Mathematics, 2005 In the present paper the Wick version of analytic functions with respect to a one dimensional Brownian motion is shown to be closely related to the backward heat equation.
LANCONELLI, ALBERTO, LANCONELLI A
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Tạp chí Khoa họcIn this paper, we first prove that the heat equation backward in time with Neumann and integral boundary conditions is an ill-posed problem. Then, we establish a stability estimate of Hölder type for this ill-posed problem.
Nguyen Van Duc
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Null controllability of a nonlinear heat equation
Abstract and Applied Analysis, 2002 We study the internal exact null controllability of a nonlinear heat equation with homogeneous Dirichlet boundary condition. The method used combines the Kakutani fixed-point theorem and the Carleman estimates for the backward adjoint linearized system ...
G. Aniculăesei, S. Aniţa
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Stability of the solution of backward heat equation on a weak compactum
Applied Mathematics and Computation, 2000 The paper investigates the stability of the Cauchy problem for the Backward heat equation under the a priori assumption that the solution is bounded. A special metrization of the weak topology in the space L-2 and the standard Fourier series technique ...
Ozdemir, Murat, Yildiz, B
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On the backward heat problem: evaluation of the norm of ∂u∂t
International Journal of Mathematics and Mathematical Sciences, 1980 We show in this paper that ‖Δu‖=‖ut‖ is bounded ∀t≤T(0)
Yves Biollay
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A Regularization Method for Backward Heat Equation on a Rectangular Domain
Journal of Harbin University of Science and TechnologyA regularization method is proposed for the non-homogeneous backward heat equation with a space-dependent source on a two-dimensional rectangular domain. This method is an extension of a known regularization approach.
WANG Yu, SUN Wei
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A stability estimate on the regularized solution of the backward heat equation
Applied Mathematics and Computation, 2003 Inverse problems, where one looks for causes for observed or desired effects, are usually "ill-posed", i.e., their solution is not unique or unstable with respect to data perturbations.
Yetiskin, H, Sever, A, Yildiz, B
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Continuous dependence on modeling for some well-posed perturbations of the backward heat equation
Journal of Inequalities and Applications, 1999 Four different well-posed regularizations of the improperly posed Cauchy problem for the backward heat equation are investigated in order to determine whether solutions of these problems depend continuously on a perturbation parameter.
Payne LE, Ames KA
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