A reaction-diffusion equation on a net-shaped thin domain

Thomas Elsken

Displaying similar documents to “A reaction-diffusion equation on a net-shaped thin domain”

On continuous and discrete maximum/minimum principles for reaction-diffusion problems with the Neumann boundary condition

Faragó, István, Korotov, Sergey, Szabó, Tamás

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In this work, we present and discuss continuous and discrete maximum/minimum principles for reaction-diffusion problems with the Neumann boundary condition solved by the finite element and finite difference methods.

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.

Diffusion and cross-diffusion in pattern formation

Wei-Ming Ni (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as $2 \times 2$ systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.

Visualization of the Reaction Zone Spreading for an Alumothermic (Redox) Reaction

Liljana Stefanovska, Toma Grcev, Sonja Gegovska-Zajkova (2002)

Visual Mathematics

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Saddle-shaped solutions of bistable diffusion equations in all of ℝ2m

Xavier Cabré, Joana Terra (2009)

Journal of the European Mathematical Society

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Diffusion of Zinc in Doped NaCl Crystals

Viera Paulíny-Tothová (1966)

Matematicko-fyzikálny časopis

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Global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients and nonhomogeneous boundary conditions.

Kouachi, Said (2002)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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$N$ -widths for singularly perturbed problems

Martin Stynes, R. Bruce Kellogg (2002)

Mathematica Bohemica

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Kolmogorov $N$ -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the $N$ -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.

Superconvergence for convection-diffusion problems with low regularity

Ludwig, Lars, Roos, Hans-Görg

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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...