Qualitative analysis of nonregular differential-algebraic equations and the dynamics of gas networks

TL;DR

This paper analyzes the mathematical properties of nonregular differential-algebraic equations, establishing conditions for solutions' existence, uniqueness, and boundedness, with applications to gas network models.

Contribution

It provides new theoretical conditions for solution behavior of nonregular differential-algebraic equations and applies these results to isothermal gas network models.

Findings

Conditions for existence, uniqueness, and boundedness of solutions are derived.

Demonstrated application to gas network models.

Insights into solution blow-up scenarios.

Abstract

The conditions for the existence, uniqueness and boundedness of global solutions, as well as ultimate boundedness of solutions, and the conditions for the blow-up of solutions of nonregular semilinear differential-algebraic equations are obtained. An example demonstrating the application of the obtained results is considered. Isothermal models of gas networks are proposed as applications.