Solvability of the heat equation with a nonlinear boundary condition

TL;DR

This paper investigates the conditions under which the heat equation with a nonlinear boundary condition in a half-space is solvable, analyzing how initial data influences the lifespan of solutions.

Contribution

It provides necessary and sufficient conditions for solvability and explores the link between initial data behavior and solution lifespan.

Findings

Derived criteria for heat equation solvability with nonlinear boundary conditions

Established relationship between initial function behavior and solution lifespan

Identified key factors affecting solution existence in half-space domains

Abstract

We obtain necessary conditions and sufficient conditions for the solvability of the heat equation in a half-space of ${\bf R}^N$ with a nonlinear boundary condition. Furthermore, we study the relationship between the life span of the solution and the behavior of the initial function.