Sharp norm estimates for the classical heat equation

TL;DR

This paper establishes precise $L^p$ norm estimates for solutions to the classical heat equation on the real line, providing sharp bounds that improve understanding of the equation's behavior.

Contribution

It introduces sharp $L^p$ norm estimates for the classical heat equation solutions, advancing the theoretical understanding of heat distribution analysis.

Findings

Derived optimal $L^p$ bounds for heat equation solutions

Enhanced understanding of heat equation behavior in $L^p$ spaces

Provided tools for further analysis of PDEs in mathematical physics

Abstract

Sharp estimates of solutions of the classical heat equation are proved in $L^p$ norms on the real line.