Related papers: Existence and Non-existence for Continuous General…
In this article, we investigate the existence and uniqueness of weak solutions to the continuous coagulation equation with collisional breakage for a class of unbounded collision kernels and distribution function. The collision kernels and…
Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and…
The causal set approach to the problem of quantum gravity is based on the hypothesis that spacetime is fundamentally discrete. Spacetime discreteness opens the door to novel types of dynamical law for cosmology and the Classical Sequential…
We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of…
The aim of this work is to study the global existence of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a triangular matrix diffusion and we show…
We present a theoretical model for the evolution of mass, angular momentum and size of galaxy disks and bulges, and we implement it into the semi-analytic galaxy formation code SAGE. The model follows both secular and violent evolutionary…
This paper deals with the fully parabolic chemotaxis system of local sensing in higher dimensions. Despite the striking similarity between this system and the Keller--Segel system, we prove the absence of finite-time blow-up phenomenon in…
A number of macroeconomic theories, very popular in the 1980s, seem to have completely disappeared and been replaced by the dynamic stochastic general equilibrium (DSGE) approach. We will argue that this replacement is due to a tacit…
In this paper we construct classical solutions of a family of coagulation equations with homogeneous kernels that exhibit the behaviour known as gelation. This behaviour consists in the loss of mass due to the fact that some of the…
In order to investigate the origin of multiple stellar populations found in globular clusters (GCs) in the halo and bulge of the Milky Way, we have constructed chemical evolution models for their putative low-mass progenitors. In light of…
Giant molecular clouds (GMCs) are well-studied in the local Universe, however, exactly how their properties vary during galaxy evolution is poorly understood due to challenging resolution requirements, both observational and computational.…
The goal of the present paper is to explore the long-time behavior of the growth-fragmentation equation formulated in the case of equal mitosis and variability in growth rate, under fairly general assumptions on the coefficients. The first…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We introduce and analyse a mathematical model describing the dynamics of particles generated by charge-exchange interactions. The model extends the well-established exchange-driven growth model, previously studied in several works, by…
We consider the homogeneous integro-differential equation$\partial \_t u=J*u-u+f(u)$ with a monostable nonlinearity $f$. Our interest is twofold: we investigate the existence/non existence of travelling waves, and the propagation properties…
The growth of large scale structure is studied in a universe containing both cold dark matter (CDM) and generalized Chaplygin gas (GCg). GCg is assumed to contribute only to the background evolution of the universe while the CDM component…
We give a comprehensive rate equation description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j,…
The galilean genesis scenario is an alternative to inflation in which the universe starts expanding from Minkowski in the asymptotic past by violating the null energy condition stably. Several concrete models of galilean genesis have been…
To take initial correlations into account, a method, based on the time-independent projection operator technique, that allows converting the conventional linear inhomogeneous (containing a source caused by initial correlations)…
We describe the onset of condensation in the simple model for the balance between selection and mutation given by Kingman in terms of a scaling limit theorem. Loosely speaking, this shows that the wave moving towards genes of maximal…