Related papers: Local existence of a solution to a free boundary p…
In many industrial applications, rubber-based materials are routinely used in conjunction with various penetrants or diluents in gaseous or liquid form. It is of interest to estimate theoretically the penetration depth as well as the amount…
We propose a moving-boundary scenario to model the penetration of diffusants into dense and foamed rubbers. The presented modelling approach recovers experimental findings related to the diffusion of cyclohexane and the resulting swelling…
For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front,…
We consider a moving boundary problem with kinetic condition that describes the diffusion of solvent into rubber and study semi-discrete finite element approximations of the corresponding weak solutions. We report on both a priori and a…
We present a fully discrete scheme for the numerical approximation of a moving-boundary problem describing diffusants penetration into rubber. Our scheme utilizes the Galerkin finite element method for the space discretization combined with…
We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the…
In this paper, we first consider two scalar nonlocal diffusion problems with a free boundary and a fixed boundary. We obtain the global existence, uniqueness and longtime behaviour of solution of these two problems. The spreading-vanishing…
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…
This short paper concerns a diffusive logistic equation with the heterogeneous environment and a free boundary, which is formulated to study the spread of an invasive species, where the free boundary represents the expanding front. A…
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…
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…
This is part II of our study on the free boundary problems with nonlocal and local diffusions. In part I, we obtained the existence, uniqueness, regularity and estimates of global solution. In part II here, we show a spreading-vanishing…
In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.
This paper concerns the free boundary problem of an epidemic model. The spatial movements of the infectious agents and the infective humans are approximated by nonlocal diffusion operators. Especially, both the growth rate of the agents and…
This paper concerns a diffusive logistic equation with a free boundary and sign-changing intrinsic growth rate in heterogeneous time-periodic environment, in which the variable intrinsic growth rate may be "very negative" in a "suitable…
This paper deals with a free boundary problem of the Lotka-Volterra type prey-predator model with variable intrinsic growth rate for predator over a one dimensional habitat, in which the free boundary represents the spreading front and is…
Motivated by a nonlocal free boundary problem, we study uniform properties of solutions to a singular perturbation problem for a boundary-reaction-diffusion equation, where the reaction term is of combustion type. This boundary problem is…
This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is introduced and studied. The model describes some mechanisms…
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…
In this paper, we propose a novel free boundary problem to model the movement of single species with a range boundary. The spatial movement and birth/death processes of the species found within the range boundary are assumed to be governed…