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

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.

Keywords

• Continuous dependence
• Modeling
• Differential inequalities
• Regularization
• Backward heat equation