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Regular version of the site

Article

Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics

Mathematische Nachrichten. 2012. Vol. 285. No. 4. P. 426-439.
Albeverio S., Danilov V.

Using an idea going back to Madelung, we construct global in time solutions to the transport equation corresponding to the asymptotic solution of the Kolmogorov-Feller equation describing a system with diffusion, potential and jump terms. To do that we use the construction of a generalized delta-shock solution of the continuity equation for a discontinuous velocity field.We also discuss corresponding problem of asymptotic solution construction (Maslov tunnel asymptotics).