Exact solutions of hyperbolic systems of kinetic equations. Application to Verhulst model with random perturbation

Details Exact solutions of hyperbolic systems of kinetic equations. Application to Verhulst model with random perturbation Exact solutions of hyperbolic systems of kinetic equations. Application to Verhulst model with random perturbation

2006-12-27

arxiv.org/abs/math/0612793v1

Mathematics

Analysis of PDEs

LaTeX2e, 13 pages

Scientific paper

For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form non-stationary solutions. The methods used include the classical Laplace cascade method as well as its recent generalizations for systems with more than 2 equations and more than 2 independent variables. As an example we present the complete non-stationary solution (probability distribution) for Verhulst model driven by Markovian coloured dichotomous noise.

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