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Abstract

In this paper, we study a Cauchy problem for the heat equation with linear source in the form ut(x,t)= uxx(x,t)+f(x,t), u(L,t)=  φ(t), u(L,t)= Ψ (t), (x,t) ∈ (0,L) ×(0, 2π). This problem is ill-posed in the sense of Hadamard. To regularize the problem, the truncation method is proposed to solve the problem in the presence of noisy Cauchy data φε and Ψε satisfying ‖ φε - φ ‖+‖ Ψε - Ψ ‖ ≤ ε and that fε satisfying ‖ fε(x,. ) - f(x,.) ‖ ≤ ε .  We give some error estimates between the regularized solution and the exact solution under some different a-priori conditions of exact solution.



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Article Details

Issue: Vol 1 No T5 (2017)
Page No.: 184-192
Published: Nov 29, 2018
Section: Original Research
DOI: https://doi.org/10.32508/stdjns.v1iT5.552

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Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 How to Cite
Vo, A., & Nguyen, T. (2018). Regularization of a Cauchy problem for the heat equation. Science and Technology Development Journal - Natural Sciences, 1(T5), 184-192. https://doi.org/https://doi.org/10.32508/stdjns.v1iT5.552

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