Journal of Inequalities and Applications 
Volume 3 (1999), Issue 1, Pages 51-64
doi:10.1155/S1025583499000041

Continuous dependence on modeling for some well-posed perturbations of the backward heat equation

K. A. Ames1 and L. E. Payne2

 1Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville 35899, AL, USA
2Department of Mathematics, Cornell University, Ithaca 14853, NY, USA
Received 14 July 1997; Revised 30 September 1997

Abstract

Four different well-posed regularizations of the improperly posed Cauchy problem for the backward heat equation are investigated in order to determine whether solutions of these problems depend continuously on a perturbation parameter. Using differential inequality techniques, we derive results implying continuous dependence in each case.