This book is devoted to positive linear dynamical systems appearing frequently in
mathematical models of various real-life problems. Here we present an operator theoretic …

We explain how operator semigroups can be used to study transport processes in networks.
This method is applied to a linear Boltzmann equation on a finite as well as on an infinite …

We study a transport equation in a network and control it in a single vertex. We describe all
possible reachable states and prove a criterion of Kalman type for those vertices in which …

We study hyperbolic systems of one-dimensional partial differential equations under
general, possibly non-local boundary conditions. A large class of evolution equations, either …

In this paper we consider a general macro-model describing a metapopulation consisting of
several interacting with each other subpopulations connected through a network, with the …

We consider singularly perturbed convection–diffusion equations on one‐dimensional
networks (metric graphs) as well as the transport problems arising in the vanishing diffusion …

In this paper we extend some of the previous results for a system of transport equations on a
closed network. We consider the Cauchy problem for a flow on a reducible network; that is, a …

The famous 1960s Lumer–Phillips theorem states that a closed and densely defined
operator AWD. A/Â X! X on a Banach space X generates a strongly continuous contraction …

We present the operator semigroups approach to the first-and second-order dynamical
systems taking place on metric graphs. We briefly survey the existing results and focus on …

Using the semigroup approach to abstract boundary control problems we characterize the
space of all exactly reachable states. Moreover, we study the situation when the controls of …