Related papers: A free boundary model for oxygen diffusion in a sp…
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…
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…
We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as…
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…
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.
The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…
This paper is mainly concerned with the free boundary problem for an approximate model (for example, arising from the study of sonoluminescence) of a gas bubble of finite mass enclosed within a bounded incompressible viscous liquid,…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
We study a toy model for the evolution of the oxygen concentration in an oxide layer. It consists in a transient convection diffusion equation in a one-dimensional domain of variable width. The motions of the boundaries are governed by the…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
In this paper we are interested with a strongly coupled system of partial differential equations that modelizes free convection in a two-dimensional bounded domain filled with a fluid saturated porous medium. This model is inspired by the…
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…
We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…
In this paper, we study the consumption-chemotaxis-Stokes model with porous medium slow diffusion in a three dimensional bounded domain with zero-flux boundary conditions and no-slip boundary condition. In recent ten years, many efforts…
The flow of a gas through porous medium is considered in the case of pressure dependent permeability. Approximate self-similar solutions of the boundary-value problems are found.
We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free boundary in a spherically symmetric setting. This free boundary…
In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…
This paper concerns compressible subsonic jet flows for a given surrounding pressure from a two-dimensional finitely long convergent nozzle with straight solid wall, which are governed by a free boundary problem for a quasilinear elliptic…
The Oxygen Depletion problem is an implicit free boundary value problem. The dynamics allow topological changes in the free boundary. We show several mathematical formulations of this model from the literature and give a new formulation…