Well-posedness of networks for 1-D hyperbolic partial differential equations

TL;DR

This paper investigates the conditions under which certain 1-D hyperbolic PDE networks are well-posed, including transport, wave, and beam equations, by deriving criteria for contraction semigroup generation.

Contribution

It provides new equivalent conditions for the well-posedness of hyperbolic PDE networks on finite intervals and semi-axes, expanding understanding of their mathematical properties.

Findings

Derived conditions for contraction semigroup generation

Established well-posedness criteria for PDE networks on finite intervals

Extended analysis to semi-axis domain

Abstract

We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even combinations of these. Equivalent conditions for contraction semigroup generation are derived. In the first part we assume a finite interval and in the second part, we consider partial differential equations on the semi-axis.