1,455 research outputs found
Substochastic semigroups and densities of piecewise deterministic Markov processes
Necessary and sufficient conditions are given for a substochastic semigroup
on obtained through the Kato--Voigt perturbation theorem to be either
stochastic or strongly stable. We show how such semigroups are related to
piecewise deterministic Markov process, provide a probabilistic interpretation
of our results, and apply them to fragmentation equations.Comment: 26 pages; corrected typo
Global strict solutions to continuous coagulationāfragmentation 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
A singular limit for an age structured mutation problem
The spread of a particular trait in a cell population often is modelled by an
appropriate system of ordinary differential equations describing how the sizes
of subpopulations of the cells with the same genome change in time. On the
other hand, it is recognized that cells have their own vital dynamics and
mutations, leading to changes in their genome, mostly occurring during the cell
division at the end of its life cycle. In this context, the process is
described by a system of McKendrick type equations which resembles a network
transport problem. In this paper we show that, under an appropriate scaling of
the latter, these two descriptions are asymptotically equivalent
Delayed stability switches in singularly perturbed predator-prey models
In this paper we provide an elementary proof of the existence of canard
solutions for a class of singularly perturbed predator-prey planar systems in
which there occurs a transcritical bifurcation of quasi steady states. The
proof uses a one-dimensional theory of canard solutions developed by V. F.
Butuzov, N. N. Nefedov and K. R. Schneider, and an appropriate monotonicity
assumption on the vector field to extend it to the two-dimensional case. The
result is applied to identify all possible predator-prey models with quadratic
vector fields allowing for the existence of canard solutions
The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth
In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible
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 on some subspace of endowed with some general
space measure . We provide a new definition of both the transport operator
and the trace measures over the incoming and outgoing parts of 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 -semigroups solving such problems
and provide conditions fully characterizing when they are positive
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