Regularization of the backward heat equation via heatlets

Electronic Journal of Differential Equations

关键词: Ill-posed problems;    backward heat equation;    wavelets;    quasireversibility;   

DOI  :  

来源: DOAJ

【 摘 要 】

Shen and Strang [16] introduced heatletsin order to solvethe heat equation using wavelet expansions of the initial data.The advantage of this approach is that heatlets, or the heat evolutionof the wavelet basis functions, can be easily computed and stored.In this paper, we use heatlets to regularize thebackwardheat equation and, more generally, ill-posed Cauchy problems.Continuous dependence results obtained by Ames and Hughes [4]are applied to approximate stabilized solutions to ill-posed problemsthat arise from the method of quasi-reversibility.

【 授权许可】

Unknown