On a comparison theorem for parabolic equations with nonlinear boundary conditions

TL;DR

This paper introduces a novel comparison theorem for nonlinear parabolic systems with nonlinear boundary conditions, enabling comparison of solutions with different boundary types and demonstrating applications like blow-up solutions.

Contribution

A new comparison theorem for nonlinear parabolic equations with diverse boundary conditions, extending classical results and facilitating analysis of blow-up phenomena.

Findings

Comparison theorem allows solutions with different boundary conditions to be compared.

Application to existence of blow-up solutions in nonlinear parabolic systems.

Enhanced analytical tools for nonlinear boundary value problems.

Abstract

In this paper, a new type of comparison theorem is presented for some initial-boundary value problems of second order nonlinear parabolic systems with nonlinear boundary conditions. This comparison theorem has an advantage over the classical ones, since this makes it possible to compare two solutions satisfying different types of boundary conditions. Some applications are given in the last section, where the existence of blow-up solutions is shown for some nonlinear parabolic equations and systems with nonlinear boundary conditions.