Neumann Boundary Problem of Second Order Parabolic Quasi-Linear System with Variable Coefficient on a Vector Bundle

TL;DR

This paper extends classical results on second order parabolic quasi-linear systems by allowing the nonlinear terms to be controlled by a power series, broadening the scope of existing theories.

Contribution

It introduces an improved framework where the nonlinear terms are bounded by a power series, enhancing previous control conditions for such systems.

Findings

Extended the class of nonlinear terms to include power series

Established new bounds for solutions of parabolic quasi-linear systems

Broadened applicability of classical parabolic theory

Abstract

Classical results of second order parabolic quasi-linear equations always require that the nonlinear terms are controlled by a power of the unknown functions and their first derivatives. We improve the previous results. More precisely, in the present article the upper bound of nonlinear term can be extended to a power series.