基于全变差正则化方法的反热传导问题未知热源函数估计

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【Abstract】The paper investigates the estimation of heat sources intransient heat conduction problems.Due to the pathologicalnatureof this typeofinverseproblem，thetotalvariationregularizationmethodisused tostabilizethesolution.This method issuitableforsolving non smoth or discontinuous problems.Bytransforming the problem intoanoptimal control problem，theexistenceand necessryconditions forthe minimum valueofthecontrolfunctionalare established.From the necessaryconditions，thelocaluniquenessandstabilityofthe minimal elementarederived.Withoutrelying onpriorinformationabouttheformoftheheat source function，adiscretizationalgorithm isused toestimatetheheat source.Numerical experiments demonstrate the efectivenesand stabilityofthis method，andcomparisons are made with the Landweberalgorithm.

Key words】 inverse heat source; total variation regularization; Landweber iteration; optimal contr

[中图分类号]0175.26;0241.82 [文献标识码］A[文章编号]1674-3229（2025）01-0042-09

0 引言

反问题中确定未知热源已得到了大量的关注，它有很多重要的工程应用，包括设计热设备、系统和仪器等。（剩余309字）