Displaying similar documents to “Singularly perturbed telegraph equations with applications in the random walk theory.”

Wildland fire propagation modelling: A novel approach reconciling models based on moving interface methods and on reaction-diffusion equations

Kaur, Inderpreet, Mentrelli, Andrea, Bosseur, Frederic, Filippi, Jean Baptiste, Pagnini, Gianni

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A novel approach to study the propagation of fronts with random motion is presented. This approach is based on the idea to consider the motion of the front, split into a drifting part and a fluctuating part; the front position is also split correspondingly. In particular, the drifting part can be related to existing methods for moving interfaces, for example, the Eulerian level set method and the Lagrangian discrete event system specification. The fluctuating part is the result of a...

Homogenization results for a linear dynamics in random Glauber type environment

Cédric Bernardin (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider an energy conserving linear dynamics that we perturb by a Glauber dynamics with random site dependent intensity. We prove hydrodynamic limits for this non-reversible system in random media. The diffusion coefficient turns out to depend on the random field only by its statistics. The diffusion coefficient defined through the Green–Kubo formula is also studied and its convergence to some homogenized diffusion coefficient is proved.

Central Limit Theorem for Diffusion Processes in an Anisotropic Random Environment

Ernest Nieznaj (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove the central limit theorem for symmetric diffusion processes with non-zero drift in a random environment. The case of zero drift has been investigated in e.g. [18], [7]. In addition we show that the covariance matrix of the limiting Gaussian random vector corresponding to the diffusion with drift converges, as the drift vanishes, to the covariance of the homogenized diffusion with zero drift.

A Neumann problem for a convection-diffusion equation on the half-line

Piotr Biler, Grzegorz Karch (2000)

Annales Polonici Mathematici

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We study solutions to a nonlinear parabolic convection-diffusion equation on the half-line with the Neumann condition at x=0. The analysis is based on the properties of self-similar solutions to that problem.

Cluster continuous time random walks

Agnieszka Jurlewicz, Mark M. Meerschaert, Hans-Peter Scheffler (2011)

Studia Mathematica

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In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly...

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.