Orthogonal Closure Procedure for the Rst Two Moments of Reaction Transport Equations
نویسنده
چکیده
The \closure problem" is a well known and widely discussed problem in transport theory. From the full transport equation one can derive a (innnite) sequence of hyperbolic subsystems for the moments. The question arises how to close the system for the rst n moments. In case of Boltzmann equations it can be answered in the theory of extended thermodynamics. Here we consider transport equations which are relevant as models for biological populations. We present a method which allows to close the rst two moment equations. The closure leads to semilinear Cattaneo systems, which are closely related to damped wave equations. We derive estimates for the residuum. The method is used to study a chemotaxis-transport equation. We show that the 2-moment approximation is a Cattaneo-chemotaxis model which in a parabolic limit converges (formally) to the classical Keller-Segel equation.
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