相关论文: Analysis of a spherical free boundary problem mode…
We prove local existence for classical solutions of a free boundary problem which arises in one of the biological selection models proposed by Brunet and Derrida, [3]. The problem we consider describes the limit evolution of branching…
In this paper we study a free boundary problem for a ratio-dependent predator-prey system in one space dimension, with the free boundary only caused by the prey. The long time behaviors of solution are discussed. Then we establish a…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
This paper investigates the long-time dynamics of a nonlocal epidemic model with free boundaries, where a pathogen with density $u(t,x)$ and the infected humans with density $v(t,x)$ evolve according to a reaction-diffusion system with…
A horizontal $N$-dimensional plane, having a diffusion of its own, exchanges with the lower half space. There, a reaction-diffusion process, modelled by a free boundary problem, takes place. We wish to understand whether, and how, the free…
One-dimensional free boundary problem for a nonlinear diffusion - convection equation with a Dirichlet condition at fixed face $x=0$, variable in time, is considered. Throught several transformations the problem is reduced to a free…
We introduce a new lattice growth model, which we call boundary sandpile. The model amounts to potential-theoretic redistribution of a given initial mass on $\mathbb{Z}^d$ ($d\geq 2$) onto the boundary of an (a priori) unknown domain. The…
The goal of this article is to find a correct approximated solution using a polynomial of sixth degree for the free boundary problem corresponding to the diffusion of oxygen in a spherical medium with simultaneous absorption at a constant…
Consider a finite system of diffusing particles coupled through a reactive boundary. Each particle is reflected, but may react with the boundary according to a killing mechanism which depends on the current reactivity of the boundary and…
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface…
A conservation-consistent boundary condition is proposed for nonlinear models of soluble-surfactant-laden falling films, ensuring exact conservation of total surfactant mass. The formulation resolves an inconsistency in widely used reduced…
The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium.…
We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
A two-dimensional free boundary model for the growth of multi-layer tumors has been proposed in [S. Cui, J. Escher: ARMA 191 (2009) 173-193] where the authors derive well-posedness in a functional analytic setting, the stationary solutions…
We present a solution of the problem of a free massless scalar field on the half line interacting through a periodic potential on the boundary. For a critical value of the period, this system is a conformal field theory with a non-trivial…
We investigate the stability and global existence of weak solutions to a free boundary problem governing the evolution of polymeric fluids. We construct weak solutions of the two-phase model by performing the asymptotic limit of a…
A continuum grain boundary model is developed that uses experimentally measured grain boundary energy data as a function of misorientation to simulate idealized grain boundary evolution in a 1-D grain array. The model uses a continuum…
An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of…
It is an interesting and important topic to study the motion of small particles in a viscous liquid in current applied research. In this paper we assume the particles are convex with arbitrary shapes and mainly investigate the interaction…