# Conditional stability for backward parabolic operators with Osgood continuous coefficients

## TL;DR

This paper establishes continuous dependence on initial data for backward parabolic operators with Osgood continuous coefficients, bridging the gap between existing uniqueness and stability results in the field.

## Contribution

It introduces a new stability result for backward parabolic operators with Osgood continuous coefficients, expanding the understanding of their well-posedness.

## Key findings

- Proves continuous dependence on initial data for a class of backward parabolic operators.
- Fills a theoretical gap between previous uniqueness and stability results.
- Enhances the mathematical framework for analyzing backward parabolic equations.

## Abstract

We prove continuous dependence on initial data for a backward parabolic operator whose leading coefficients are Osgodd continuous in time. This result fills the gap between uniqueness and continuity results obtained so far.