Related papers: Boundary value for a nonlinear transport equation …
This papers addresses the connection between two classical models of phase transition phenomena describing different stages of the growth of clusters. The Becker-D\"oring model (BD) describes discrete-sized clusters through an infinite set…
We prove existence and uniqueness of solutions to the initial-boundary value problem for the Lifshitz--Slyozov equation (a nonlinear transport equation on the half-line), focusing on the case of kinetic rates with unbounded derivative at…
This paper is concerned with the initial-boundary value problem \; for stochastic transport equations in bounded domains. For a given stochastic perturbation of the drift vector field, we prove existence and uniqueness of weak solutions…
The coarsening dynamics of the Cahn-Hilliard equation with order-parameter dependent mobility, $\lambda(\phi) \propto (1-\phi^2)^\alpha$, is addressed at zero temperature in the Lifshitz-Slyozov limit where the minority phase occupies a…
We present a survey on the results on a particular coagulation-fragmentation model given by the Becker-D\"oring equations. For both the deterministic and stochastic versions, we include well-posedness, long-time behavior, convergence rate…
We aim at quantitatively determining transport parameters like conductivity, mean free path, etc., for simple models of spatially completely disordered quantum systems, comparable to the systems which are sometimes referred to as Lifshitz…
We prove that the stochastic Burgers equation, which is related to the Kardar-Parisi-Zhang/KPZ equation via weak derivative, is a "critical" scaling limit for density fluctuations for a family of non-integrable and non-stationary…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
In this paper, we study the initial-boundary value problem for the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with Stratonovich-type noise in bounded domains $\mathcal{O}\subset\mathbb{R}^d$, $d=1,2,3$. Our main results can be…
Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a stochastic and non-linear extension of the…
We study nonequilibrium steady states of a one-dimensional stochastic model, originally introduced as an approximation of the Discrete Nonlinear Schr\"odinger equation. This model is characterized by two conserved quantities, namely mass…
We show existence of a regular solution in Sobolev-Slobodetskii spaces to stationary transport equation with inflow boundary condition in a bounded domain $\Omega \subset \mathbb{R}^2$. Our result is subject to quite general constraint on…
In this note, we study an infinite reaction network called the stochastic Becker-D\"oring process, a sub-class of the general coagulation-fragmentation models. We prove pathwise convergence of the process towards the deterministic…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
Finite size consideration of matter significantly affects transport coefficients like shear viscosity, bulk viscosity, electrical conductivity, which we have investigated here in the framework of the Polyakov-Nambu-Jona-Lasinio model. Owing…
Understanding the transport properties of quantum many-body systems is a central challenge in condensed matter and statistical physics. Theoretical studies usually rely on two main approaches: Dynamics of linear-response functions in closed…
To model the dynamics of polymers formed through nucleation, elongated by polymerisation, shortened by depolymerisation and subject to aggregation reactions, we study a nonlinear integro-differential equation. Growth and shrinkage are…
A stochastic free-boundary problem for the three-dimensional barotropic compressible Navier--Stokes equations is studied. The main feature of the model is that the free boundary is transported by a Stratonovich stochastic flow, so that the…
In this work, we consider the fractional Stefan-type problem in a Lipschitz bounded domain $\Omega\subset\mathbb{R}^d$ with time-dependent Dirichlet boundary condition for the temperature $\vartheta=\vartheta(x,t)$, $\vartheta=g$ on…
This paper considers the neutron transport equation in bounded domain with a combination of the diffusive boundary condition and the in-flow boundary condition. We firstly study the existence of solution in any fixed time by…