Displaying similar documents to “Diffusion and cross-diffusion in pattern formation”

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....

On the number of stationary patterns in reaction-diffusion systems

Rybář, Vojtěch, Vejchodský, Tomáš

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We study systems of two nonlinear reaction-diffusion partial differential equations undergoing diffusion driven instability. Such systems may have spatially inhomogeneous stationary solutions called Turing patterns. These solutions are typically non-unique and it is not clear how many of them exists. Since there are no analytical results available, we look for the number of distinct stationary solutions numerically. As a typical example, we investigate the reaction-diffusion system designed...

Inverse Problems for Parabolic Equation with Discontinuous Coefficients

V. Dinakar, N. Barani Balan, K. Balachandran (2017)

Nonautonomous Dynamical Systems

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We consider the reaction-diffusion equation with discontinuities in the diffusion coefficient and the potential term. We start by deriving the Carleman estimate for the discontinuous reaction-diffusion operator which is deployed in the inverse problems of finding the stability result of the two discontinuous coefficients from the internal observations of the given parabolic equation.

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...

Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory

Salah Badraoui (1999)

Applicationes Mathematicae

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We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.