Global strict solutions to continuous coagulation–fragmentation equations with strong fragmentation

In this paper we give an elementary proof of the unique, global-in-time solvability of the coagulation-(multiple) fragmentation equation with polynomially bounded fragmentation and particle production rates and a bounded coagulation rate. The proof relies on a new result concerning domain invariance for the fragmentation semigroup which is based on a simple monotonicity argument

Coagulation, fragmentation and growth processes in a size structured population

An equation describing the dynamical behaviour of hytoplankton cells is considered in which the effects of cell division and aggregration are incorporated by coupling the coagulationfragmentation equation with the McKendrick-von Foerster renewal model of an age-structured population. Under appropriate conditions on the model parameters, the associated initial boundary value problem is shown to be well posed in a physically relevant Banach space

On L2-solvability of mixed boundary value problems for elliptic equations in plane non-smooth domains

AbstractThis paper is devoted to an L2-solvability of mixed boundary value problems (MBVPs) for second order elliptic equations in plane domains with curvilinear polygons as its boundaries. We find a space T′ such that the MBVP with data in L2(Ω) × T′ is solvable in L2(Ω) and calculate the dimension of the kernel of this problem. Moreover we relate our approach to the previous one [P. Grisvard, “Elliptic Boundary Problems in Non-smooth Domains,” Pitman, New York, 1985] showing how to overcome difficulties arising there

Logarithmic norms and regular perturbations of differential equations

In this note we explore the concept of the logarithmic norm of a matrix and illustrate its applicability by using it to find conditions under which the convergence of solutions of regularly perturbed systems of ordinary differential equations is uniform globally in time

A new approach to transport equations associated to a regular field: trace results and well-posedness

We generalize known results on transport equations associated to a Lipschitz field $\mathbf{F}$ on some subspace of $\mathbb{R}^N$ endowed with some general space measure $\mu$. We provide a new definition of both the transport operator and the trace measures over the incoming and outgoing parts of $\partial \Omega$ generalizing known results from the literature. We also prove the well-posedness of some suitable boundary-value transport problems and describe in full generality the generator of the transport semigroup with no-incoming boundary conditions.Comment: 30 page

Semigroup approach to diffusion and transport problems on networks

Models describing transport and diffusion processes occurring along the edges of a graph and interlinked by its vertices have been recently receiving a considerable attention. In this paper we generalize such models and consider a network of transport or diffusion operators defined on one dimensional domains and connected through boundary conditions linking the end-points of these domains in an arbitrary way (not necessarily as the edges of a graph are connected). We prove the existence of $C_0$-semigroups solving such problems and provide conditions fully characterizing when they are positive