Related papers: Diffusion, Fragmentation and Coagulation Processes…
In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…
Fragmentation--coagulation processes, in which aggregates can break up or get together, often occur together with decay processes in which the components can be removed from the aggregates by a chemical reaction, evaporation, dissolution,…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
A hierarchical system of equations is introduced to describe dynamics of `sizes' of infinite clusters which coagulate and fragmentate with homogeneous rates of certain form. We prove that this system of equations is solved weakly by…
In the paper, we study spatially distributed particle systems whose time evolution is governed by vanishing diffusion in space $\mathbb{R}^d$, $d\ge 1$, and by size-continuous fragmentation and coagulation processes with unbounded rates. We…
We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential…
We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition.…
Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process…
We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we…
We are interested in the large time behavior of the solutions to the growth-fragmentation equation. We work in the space of integrable functions weighted with the principal dual eigenfunction of the growth-fragmentation operator. This space…
We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show…
In this paper, we consider a continuous fragmentation--coagulation model in which the reacting particles can be transported in physical space through either advection or diffusion. We prove new results on the generation of $C_0$-semigroups…
We review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics. The problems in continuum mechanics concern mathematical…
We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval $[0,T]$ sampled with a time step $\Delta$. Our main contribution…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
We report accelerating diffusive solutions to the diffusion equation with a constant diffusion tensor. The maximum values of the diffusion density evolve in an accelerating fashion described by Airy functions. We show the diffusive…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…