Diffusion from a Bottom Layer; Diffusion with Moving Boundaries.

Simulating Stochastic Reaction-Diffusion Systems on and within Moving Boundaries

Chemical reactions inside cells are generally considered to happen within fixed-size compartments. However, cells and their compartments are highly dynamic. Thus, such stringent geometrical assumptions may not reflect biophysical reality, and can highly bias conclusions from simulation studies. In this work, we present an intuitive algorithm for particle-based diffusion in and on moving boundar...

7A Diffusion in domains with switching boundaries

In the analysis of narrow escape problems in Sect. 7.2, we assumed that the holes in the boundary of the domain were always open. However, if we view each pore as a stochastically gated ion channel, for example, then one has the problem of analyzing the diffusion equation in a domain with a randomly switching boundary (or partial boundary). Such a scenario also arises in the case of membrane di...

A singularly perturbed convection – diffusion problem with a moving interior layer ∗

A singularly perturbed parabolic equation of convection-diffusion type with an interior layer in the initial condition is studied. The solution is decomposed into a discontinuous regular component, a continuous outflow boundary layer component and a discontinuous interior layer component. A priori parameter-explicit bounds are derived on the derivatives of these three components. Based on these...

Moving Boundary Problems with Nonlinear Diffusion

A Diffusion Equation with Exponential Nonlinearity Recant Developments

The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...