Existence of asymptotic speed of solutions to birth and spread type nonlinear partial differential equations

TL;DR

This paper proves the existence of a well-defined asymptotic speed for solutions to a broad class of nonlinear parabolic PDEs, providing explicit examples, properties, and numerical insights.

Contribution

It establishes the existence of asymptotic speed for fully nonlinear, possibly degenerate parabolic PDEs in a general framework, with detailed examples and numerical analysis.

Findings

Existence of asymptotic speed for solutions to nonlinear PDEs

Explicit examples illustrating the theory

Numerical results supporting the theoretical findings

Abstract

In this paper, we prove the existence of asymptotic speed of solutions to fully nonlinear, possibly degenerate parabolic partial differential equations in a general setting. We then give some explicit examples of equations in this setting and study further properties of the asymptotic speed for each equation. Some numerical results concerning the asymptotic speed are presented.