Life Span of Solutions for a Semilinear Heat Equation with Initial Data Non-Rarefied at $\infty$

TL;DR

This paper investigates how non-rarefied initial data at infinity influences the lifespan of solutions to a semilinear heat equation, providing sharp estimates and insights into the solution's longevity.

Contribution

It introduces new sharp estimates on the lifespan of solutions considering non-rarefied initial data at infinity, advancing understanding of solution behavior in such conditions.

Findings

Sharp lifespan estimates for solutions with non-rarefied initial data

Demonstrates the impact of non-rarefied factors on solution longevity

Provides analytical tools for lifespan analysis in semilinear heat equations

Abstract

We study the Cauchy problem for a semilinear heat equation with initial data non-rarefied at $\infty$. Our interest lies in the discussion of the effect of the non-rarefied factors on the life span of solutions, and some sharp estimates on the life span is established.