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