Displaying similar documents to “Hypocoercive Diffusion Operators”

Some remarks concerning stabilization techniques for convection--diffusion problems

Brandner, Marek, Knobloch, Petr

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There are many methods and approaches to solving convection--diffusion problems. For those who want to solve such problems the situation is very confusing and it is very difficult to choose the right method. The aim of this short overview is to provide basic guidelines and to mention the common features of different methods. We place particular emphasis on the concept of linear and non-linear stabilization and its implementation within different approaches.

Fast optical tracking of diffusion in time-dependent environment of brain extracellular space

Hrabě, Jan

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An improved version of the Integrative Optical Imaging (IOI) method for diffusion measurements in a geometrically complex environment of the brain extracellular space has been developed. We present a theory for this Fast Optical Tracking Of Diffusion (FOTOD) which incorporates a time-dependent effective diffusion coefficient in homogeneous anisotropic media with time-dependent nonspecific linear clearance. FOTOD can be used to measure rapid changes in extracellular diffusion permeability...

Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation

Thierry Goudon, Antoine Mellet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.

A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems

Hideki Murakawa (2009)

Kybernetika

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This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems....

Convergence and stability of higher-order finite element solution of reaction-diffusion equation with Turing instability

Kůs, Pavel

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In this contribution, higher-order finite element method is used for the solution of reaction-diffusion equation with Turing instability. Some aspects concerning convergence of the method for this particular problem are discussed. Our numerical tests confirm the convergence of the method, but for some very special choices of parameters, this convergence has very uncommon properties.

Solution of contaminant transport with adsorption in porous media by the method of characteristics

Jozef Kacur, Roger Van Keer (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.