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[visio] Asymptotic solutions of singular perturbed system of transport equations with small mutual diffusion in the case of many spatial variables
1 : Russian University of Economics. G. V. Plekhanov
("REU them. G. V. Plekhanov»)
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Russia
We construct an asymptotic expansion on a small parameter of the solution of the Cauchy problem for a singularly perturbed system of transport equations with small nonlinearity and mutual diffusion describing the transport in a multiphase medium for many spatial variables. The asymptotic expansion of the solution is constructed as a series in powers of a small parameter and contains a functions of the boundary and inner layers. The main part of the asymptotics is described by one equation, which under certain requirements on the nonlinearity and diffusion terms is a generalization of the equation Burgers -Korteweg-de Vries in the case of many spatial variables.
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