On the Mathematical Modeling of an Infinitecomponent Mixture.
Professor Mikhail ZhukovSouth Federal University, Russia 下午 3:00–3:50 鴻經館 107 室To describe a multicomponent mixture with the large number of components we use formal transition from multicomponent mixture to infinitecomponent mixture. The discrete set of concentrations dependent on a discrete index k is replaced by distribution function of continuous parameter (sort parameter). Similarly, the kinetic coefficients characterizing a mixture (diffusion coefficients, mobility coefficients, etc.) are replaced by distribution functions of sort parameter. In this case the system of equations is replaced by only one equation dependent on sort parameter. For correct replacement it is required the constructing of S-space with additive measure (space of sort parameter). ),(txuk),,(txkuk
Several examples solved with help such approach to problem are presented.
1. Construction the Riemann invariants for the hyperbolic equations (mass transfer under action of an electric field).
2. The problem of hydrodynamic stability (concentration gravitational convection in a layer of a liquid).
3. Stationary distribution of concentration in infinitecomponent mixture