Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 130, pp. 1-8.

Title: Regularization of the backward heat equation via heatlets
  
Authors: Beth Marie Campbell Hetrick (Gettysburg College, PA, USA)
         Rhonda Hughes (Bryn Mawr College, USA)
	 Emily McNabb  (Bryn Mawr College, USA)

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