Displaying similar documents to “Arnold diffusion: a variational construction.”

A variational approach to bifurcation points of a reaction-diffusion system with obstacles and Neumann boundary conditions

Jan Eisner, Milan Kučera, Martin Väth (2016)

Applications of Mathematics

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Given a reaction-diffusion system which exhibits Turing's diffusion-driven instability, the influence of unilateral obstacles of opposite sign (source and sink) on bifurcation and critical points is studied. In particular, in some cases it is shown that spatially nonhomogeneous stationary solutions (spatial patterns) bifurcate from a basic spatially homogeneous steady state for an arbitrarily small ratio of diffusions of inhibitor and activator, while a sufficiently large ratio is necessary...

Solution of degenerate parabolic variational inequalities with convection

Jozef Kacur, Roger Van Keer (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard's equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.

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.