# Space like strong unique continuation for sublinear parabolic equations

## TL;DR

This paper proves a space-like strong unique continuation property for certain sublinear parabolic equations, extending elliptic results using new Carleman estimates, which enhances understanding of solution behavior in these equations.

## Contribution

It introduces a novel Carleman estimate for sublinear parabolic operators and establishes a space-like strong unique continuation property, paralleling recent elliptic results.

## Key findings

- Established space-like strong unique continuation for sublinear parabolic equations.
- Developed a new $L^{2}-L^{2}$ Carleman estimate for these operators.
- Extended elliptic strong unique continuation results to the parabolic setting.

## Abstract

In this paper, we establish space like strong unique continuation property (sucp) for uniformly parabolic sublinear equations under appropriate structural assumptions. Our main result Theorem 1.1 constitutes the parabolic counterpart of the strong unique continuation result recently established by Ruland in [Ru] for analogous elliptic sublinear equations. Similar to that in [Ru], this is accomplished via a new $L^{2}-L^{2}$ type Carleman estimate for a class of sublinear parabolic operators.