TITLE

REGULARIZATION OF THE BACKWARD HEAT EQUATION VIA HEATLETS

AUTHOR(S)
CAMPBELL HETRICK, BETH MARIE; HUGHES, RHONDA; MCNABB, EMILY
PUB. DATE
April 2008
SOURCE
Electronic Journal of Differential Equations;2008, Vol. 2008, Special section p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Abstract. Shen and Strang [16] introduced heatlets in order to solve the heat equation using wavelet expansions of the initial data. The advantage of this approach is that heatlets, or the heat evolution of the wavelet basis functions, can be easily computed and stored. In this paper, we use heatlets to regularize the backward heat 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 problems that arise from the method of quasi-reversibility.
ACCESSION #
36099161

 

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