Electron. J. Diff. Eqns., Vol. 2008(2008), No. 130, pp. 1-8.

Regularization of the backward heat equation via heatlets

Beth Marie Campbell Hetrick, Rhonda Hughes, Emily McNabb

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.

Submitted March 27, 2008. Published September 18, 2008.
Math Subject Classifications: 47A52, 42C40.
Key Words: Ill-posed problems; backward heat equation; wavelets; quasireversibility

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Beth Marie Campbell Hetrick
Gettysburg College, Gettysburg, PA 17325, USA
email: bcampbel@gettysburg.edu
Rhonda Hughes
Bryn Mawr College, Bryn Mawr, PA 19010, USA
email: rhughes@brynmawr.edu
Emily McNabb
Bryn Mawr College, Bryn Mawr, PA 19010, USA
email: emily.a.mcnabb@accenture.com

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