Related papers: A free boundary problem arising from branching Bro…
This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…
The Branching Brownian Motions (BBM) are particles performing independent Brownian motions in $\mathbb R$ and each particle at rate 1 creates a new particle at her current position; the newborn particle increments and branchings are…
This work presents the existence and uniqueness of solution to a free boundary value problem related to biofilm growth. The problem consists of a system of nonlinear hyperbolic partial differential equations governing the microbial species…
A meshfree Lagrangian method for the fluctuating hydrodynamic equations (FHEs) with fluid-structure interactions is presented. Brownian motion of the particle is investigated by direct numerical simulation of the fluctuating hydrodynamic…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
We make a rigorous analysis of the existence and characterization of the free boundary related to the optimal stopping problem that maximizes the mean of an Ornstein--Uhlenbeck bridge. The result includes the Brownian bridge problem as a…
We solve two stochastic control problems in which a player tries to minimize or maximize the exit time from an interval of a Brownian particle, by controlling its drift. The player can change from one drift to another but is subject to a…
A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using…
We consider a branching-selection system in $\mathbb {R}$ with $N$ particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, keeping the number of particles constant. We show that, as…
In 2001, Knight constructed a stochastic process modeling the one dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion, and the other particle being Brownian. We construct a…
Sticky diffusion processes on bounded domains spend finite time (and finite mean time) on the lower-dimensional space given by the boundary. Once the process hits the boundary, then it starts again after a random amount of time. While on…
An asymptotic analysis of the Gunn effect in two-dimensional samples of bulk n-GaAs with circular contacts is presented. A moving pulse far from contacts is approximated by a moving free boundary separating regions where the electric…
In this paper we focus the attention on free boundary problems ruled by partial differential equations with nonstandard growth, presenting in particular some recent results. The interest in these problems stems from the diverse applications…
The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system (MEMS) is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a…
A mutualist model with nonlocal diffusions and a free boundary is first considered. We prove that this problem has a unique solution defined $t\ge0$, and its dynamics are governed by a spreading-vanishing dichotomy. Some criteria for…
We provide a rigorous derivation of the brownian motion as the limit of a deterministic system of hard-spheres as the number of particles $N$ goes to infinity and their diameter $\varepsilon$ simultaneously goes to $0$, in the fast…
A free boundary value problem related to the genesis of multispecies granular biofilms is presented. The granular biofilm is modelled as a spherical free boundary domain with radial symmetry. The proposed model is conceived in the framework…
We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the…
We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and…
We study the autophoretic motion of a spherical active particle interacting chemically and hydrodynamically with its fluctuating environment in the limit of rapid diffusion and slow viscous flow. Then, the chemical and hydrodynamic fields…