An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

A. Hazanee; D. Lesnic; M.I. Ismailov; N.B. Kerimov

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An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

机译：具有非经典边界条件的热方程的时变源反问题

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摘要

This paper investigates the inverse problem of determining the time-dependent heat source and the temperature for the heat equation with a non-classical boundary and an integral over-determination conditions. The existence, uniqueness and continuous dependence upon the data of the classical solution of the inverse problem is shown by using the generalised Fourier method. Furthermore in the numerical process, the boundary element method (BEM) together with the second-order Tikhonov regularization is employed with the choice of regularization parameter based on the generalised cross-validation (GCV) criterion. Numerical results are presented and discussed.

机译：本文研究了确定具有非经典边界和积分超确定条件的热方程的时变热源和温度的反问题。通过广义傅立叶方法，证明了反问题经典解的存在性，唯一性和对数据的连续依赖。此外，在数值过程中，边界元方法（BEM）与二阶Tikhonov正则化一起使用，基于广义交叉验证（GCV）准则选择正则化参数。提出并讨论了数值结果。

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来源
《Applied Mathematical Modelling》 |2015年第20期|6258-6272|共15页
作者
A. Hazanee; D. Lesnic; M.I. Ismailov; N.B. Kerimov;
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作者单位

Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK;

Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK;

Department of Mathematics, Gebze Institute of Technology, Gebze, Kocaeli 41400, Turkey;

Department of Mathematics, Mersin University, Mersin 33343, Turkey;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Heat equation; Inverse source problem; Non-classical boundary conditions; Generalised Fourier method;

机译：热方程;逆源问题;非经典边界条件;广义傅里叶法;

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2. Inverse Source Problem for Heat Equation with Nonlocal Wentzell Boundary Condition [J] . Ismailov Mansur I. Results in mathematics . 2018,第2期

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3. Boundaries and defects of $N = 4$ $$ mathcal{N}=4 $$ SYM with 4 supercharges. Part I: Boundary/junction conditions [J] . Akikazu Hashimoto, Peter Ouyang, Masahito Yamazaki The journal of high energy physics . 2014,第10期

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6. Near-field infinity-simulating boundary conditions for the heat equation [O] . Adi Ditkowski, Alexander Suhov 2008

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7. An inverse time-dependent source problem for the heat equation with a non-classical boundary condition [O] . Hazanee, A, Lesnic, D, Ismailov, MI, 2015

机译：具有非经典边界条件的热方程的逆时变源问题

An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

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