The global solvability of initial-boundary value problem for nondiagonal parabolic systems

TL;DR

This paper proves the global existence and well-posedness of classical solutions for quasilinear nondiagonal parabolic systems with divergence-structured elliptic operators, under certain conditions.

Contribution

It establishes the global solvability of initial-boundary value problems for a class of complex parabolic systems with divergence structure, extending prior results.

Findings

Proved well-posedness of classical solutions

Established global existence in time

Identified conditions for solvability

Abstract

In this paper we study the quasilinear nondiagonal parabolic type systems. We assume that the principal elliptic operator, which is part of the parabolic system, has a divergence structure. Under certain conditions it is proved the well-posedness of classical solutions, which exist globally in time.