文章基本信息

标题：A filter method for inverse nonlinear sideways heat equation
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作者：Nguyen Anh Triet ; Donal O’Regan ; Dumitru Baleanu 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-18
DOI：10.1186/s13662-020-02601-4
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study a sideways heat equation with a nonlinear source in a bounded domain, in which the Cauchy data at $x = \mathcal {X}$ are given and the solution in $0 \le x < \mathcal {X}$ is sought. The problem is severely ill-posed in the sense of Hadamard. Based on the fundamental solution to the sideways heat equation, we propose to solve this problem by the filter method of degree α, which generates a well-posed integral equation. Moreover, we show that its solution converges to the exact solution uniformly and strongly in $\mathscr {L}^{p}(\omega,\mathcal {X};\mathscr {L}^,(\mathbb {R}))$, $\omega\in [0,\mathcal {X})$ under a priori assumptions on the exact solution. The proposed regularized method is illustrated by numerical results in the final section.
关键词：Backward problem;Nonlinear heat equation;Ill-posed problem;Cauchy problem;Regularization method;Error estimate;