%0 Journal Article
%T Exact solutions of hyperbolic systems of kinetic equations. Application to Verhulst model with random perturbation
%A E. I. Ganzha
%A V. M. Loginov
%A S. P. Tsarev
%J Mathematics
%D 2006
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0612793v1