Continuous Dependence for Backward Parabolic Operators with Log-Lipschitz Coefficients

TL;DR

This paper establishes the continuous dependence of solutions on initial data for backward parabolic operators with coefficients that are Log-Lipschitz continuous in time, contributing to the stability analysis of such equations.

Contribution

It proves continuous dependence results for backward parabolic operators with Log-Lipschitz coefficients, a novel regularity condition in this context.

Findings

Proved continuous dependence on Cauchy data.

Established stability results for backward parabolic operators.

Extended understanding of regularity effects on solution stability.

Abstract

We prove continuous dependence on Cauchy data for a backward parabolic operator whose coefficients are Log-Lipschitz continuous in time.