Existence of global-in-time solutions to a system of fully nonlinear parabolic equations

TL;DR

This paper proves the existence of solutions that persist for all time to a complex system of fully nonlinear parabolic equations, under conditions tailored to this nonlinear context.

Contribution

It establishes the first known conditions guaranteeing global-in-time solutions for fully nonlinear parabolic systems.

Findings

Proved existence of global solutions under specific conditions.

Identified conditions unique to fully nonlinear systems.

Extended understanding of long-term behavior of nonlinear parabolic equations.

Abstract

We consider the Cauchy problem for a system of fully nonlinear parabolic equations. In this paper, we shall show the existence of global-in-time solutions to the problem. Our condition to ensure the global existence is specific to the fully nonlinear parabolic system.