Pointwise estimates for solutions of semilinear parabolic inequalities with a potential

TL;DR

This paper derives pointwise estimates for solutions to semilinear parabolic equations with potentials on various domains, including Euclidean spaces and Riemannian manifolds.

Contribution

It provides new pointwise bounds for solutions of semilinear parabolic inequalities with potentials on diverse geometric settings.

Findings

Establishment of pointwise estimates on Euclidean domains.

Extension of estimates to general Riemannian manifolds.

Applicable to a broad class of semilinear parabolic inequalities.

Abstract

We obtain pointwise estimates for solutions of semilinear parabolic equations with a potential on connected domains both of $\mathbb R^n$ and of general Riemannian manifolds.