Linear Boltzmann-like equation, describing non-classical particle transport, and related asymptotic solutions for small mean free paths

Abstract

In classical kinetic or kinetic-like models a particle free path distribution is exponensial, but this is more likely to be an exception than a rule. In this paper we derive a linear Boltzmann-like equation for a general free path distribution in the framework of Alt's model J. Math. Biol. 9:147 (1980). In the special case that the free path distribution has at least first and second finite moments we construct an asymptotic solution of the equation for small mean free paths. The asymptotic solution becomes a diffusion approximation to the one-speed Boltzmann-like equation.

14 pages

References in corpus (4)

• Anomalous Diffusion of Inertial, Weakly Damped Particles
• Anomalous Diffusion of Self-Propelled Particles in Directed Random Environments
• A Generalized Linear Transport Model for Spatially-Correlated Stochastic Media
• Persistent random walk of cells involving anomalous effects and random death

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