On solvability of dissipative partial differential-algebraic equations

TL;DR

This paper extends classical theorems like Hille-Yosida and Lumer-Phillips to analyze the solvability of dissipative partial differential-algebraic equations, providing new insights into their solution structure.

Contribution

It introduces an extension of the Hille-Yosida and Lumer-Phillips theorems for dissipative PDE-DAEs, broadening the theoretical framework for their solvability.

Findings

Extended Hille-Yosida theorem for PDE-DAEs

Extended Lumer-Phillips theorem for dissipative PDE-DAEs

Illustrated results with coupled systems and Dzektser equation

Abstract

In this article we investigate the solvability of infinite-dimensional differential algebraic equations. Such equations often arise as partial differential-algebraic equations (PDAEs). A decomposition of the state-space that leads to an extension of the Hille-Yosida Theorem on Hilbert spaces for these equations is described. For dissipative partial differential equations the famous Lumer-Phillips generation theorem characterizes solvability and also boundedness of the associated semigroup. An extension of the Lumer-Phillips generation theorem to dissipative differential-algebraic equations is given. The results is illustrated by coupled systems and the Dzektser equation.