How does a reflected one-dimensional diffusion bounce back?
Jean Bertoin (1992)
Forum mathematicum
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Jean Bertoin (1992)
Forum mathematicum
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Viera Paulíny-Tothová (1966)
Matematicko-fyzikálny časopis
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P. Brunovský, B. Fiedler (1987)
Banach Center Publications
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Xavier Cabré, Joana Terra (2009)
Journal of the European Mathematical Society
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Patrick Cattiaux, Christian Léonard (1995)
Forum mathematicum
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Masao Nagasawa (1993)
Séminaire de probabilités de Strasbourg
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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...
Kůs, Pavel, Dolejší, Vít
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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...
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.