Asymptotics of viscosity solutions to some doubly nonlinear parabolic equations

TL;DR

This paper investigates the long-term behavior of viscosity solutions to certain doubly nonlinear parabolic equations, including Trudinger's equation, establishing decay rates and a Phragmén-Lindelöf type result with optimality.

Contribution

It provides new asymptotic decay estimates and a Phragmén-Lindelöf principle for viscosity solutions of doubly nonlinear parabolic equations, including Trudinger's equation.

Findings

Derived decay rates for viscosity solutions.

Proved a Phragmén-Lindelöf type result.

Established the optimality of the results.

Abstract

We study asymptotic decay rates of viscosity solutions to some doubly nonlinear parabolic equations, including Trudinger's equation. We also prove a Phragm\'en-Lindel\"of type result and show its optimality.