In order to become worldly things, that is, deeds and facts and events and patterns of
thoughts or ideas,[action, speech, and thought] must first be seen, heard, and remembered …

A lot of well-known partial differential equations modeling physical systems, such as the heat
equation, the Schrödinger equation or the wave equation, use temporal change of states …

We discuss the mathematical modeling and numerical discretization of transport problems
on one-dimensional networks. Suitable coupling conditions are derived that guarantee …

We introduce a class of partial differential equations on metric graphs associated with mixed
evolution: on some edges we consider diffusion processes, and on others transport …

Our goal is to show asynchronous exponential growth (AEG) for a flow in a network with
delay in the vertices. For this purpose we show first that its wellposedness can be …

Unter einem Fluss in einem Netzwerk verstehen wir einen Transportprozess, der mittels
eines Systems linearer partieller Differentialgleichungen beschrieben wird. Die diesem …

We develop a variational approach in order to study qualitative properties of
nonautonomous parabolic equations. Based on the method of product integrals, we discuss …

In this chapter we are going to review a manifold of operators defined on networks. We will
see later on that most of these operators arise in connection with some relevant evolution …

It is well-known from elementary linear algebra that the solution of the linear Cauchy
problem\left {associated with an n× n matrix A is given by x (t):= e tA x 0, where the …