Existence and Uniqueness of Local and Global Solutions for a Partial Differential-Algebraic Equation of Index One

TL;DR

This paper proves the existence and uniqueness of local and global solutions for a specific class of partial differential-algebraic equations of index one using nonlinear semigroup theory, with applications to reaction-diffusion systems.

Contribution

It introduces a novel application of nonlinear semigroup theory to establish solution properties for index-one PDAEs, including a transformation approach for coupled systems.

Findings

Established existence and uniqueness of solutions

Applied method to reaction-diffusion coupled with elliptic equations

Demonstrated global solution existence under certain conditions

Abstract

In this paper, we use the theory of nonlinear semigroups to establish the existence and uniqueness of both local and global solutions for a partial differential-algebraic equation (PDAE) of index one. This method is applied to a reaction-diffusion system coupled with an elliptic equation in one dimension by transforming the PDAE into a system of linear evolution equations with a Lipschitz-continuous perturbation