Transport Equation on Semidiscrete Domains and Poisson-Bernoulli Processes

Details Transport Equation on Semidiscrete Domains and Poisson-Bernoulli Processes Transport Equation on Semidiscrete Domains and Poisson-Bernoulli Processes

2012-01-04

arxiv.org/abs/1201.0858v1

Mathematics

Analysis of PDEs

16 pages, 12 figures

Scientific paper

In this paper we consider a scalar transport equation with constant coefficients on domains with discrete space and continuous, discrete or general time. We show that on all these underlying domains solutions of the transport equation can conserve sign and integrals both in time and space. Detailed analysis reveals that, under some initial conditions, the solutions correspond to counting stochastic processes and related probability distributions. Consequently, the transport equation could generate various modifications of these processes and distributions and provide some insights into corresponding convergence questions. Possible applications are suggested and discussed.

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