Optimal extinction rates for the fast diffusion equation with strong absorption

TL;DR

This paper derives the optimal rates at which solutions to a fast diffusion equation with strong absorption vanish as they approach extinction time, providing precise asymptotic behavior.

Contribution

It establishes the exact extinction rates for solutions to the fast diffusion equation with strong absorption, extending previous understanding of their asymptotic behavior.

Findings

Derived explicit extinction rates for solutions.

Identified conditions for optimal extinction behavior.

Enhanced understanding of solution decay near extinction.

Abstract

Optimal extinction rates near the extinction time are derived for non-negative solutions to a fast diffusion equation with strong absorption, the power of the absorption exceeding that of the diffusion.