Quasi linear parabolic pde posed on a network with non linear Neumann boundary condition at vertices

TL;DR

This paper investigates second-order quasi-linear parabolic PDEs on networks with nonlinear Neumann boundary conditions at vertices, establishing existence and uniqueness of classical solutions.

Contribution

It introduces a framework for solving quasi-linear parabolic PDEs on networks with nonlinear boundary conditions, proving existence and uniqueness results.

Findings

Existence of classical solutions is proven.

Uniqueness of solutions is established.

Framework for PDEs on networks with nonlinear boundary conditions.

Abstract

The purpose of this article is to study quasi linear parabolic partial differential equations of second order, posed on a bounded network, satisfying a nonlinear and non dynamical Neumann boundary condition at the vertices. We prove the existence and the uniqueness of a classical solution.