Abstract.
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 new procedures 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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This paper was written with partial financial support from the RFBR grant 06-01-00814 and the DFG Research Unit 565 “Polyhedral Surfaces” (TU-Berlin).
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Ganzha, E.I., Loginov, V.M. & Tsarev, S.P. Exact Solutions of Hyperbolic Systems of Kinetic Equations. Application to Verhulst Model with Random Perturbation. Math.comput.sci. 1, 459–472 (2008). https://doi.org/10.1007/s11786-007-0036-0
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DOI: https://doi.org/10.1007/s11786-007-0036-0