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

Albeverio S, Danilov V (2012)
Mathematische Nachrichten 285(4): 426-439.

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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). (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Albeverio S, Danilov V. Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics. Mathematische Nachrichten. 2012;285(4):426-439.
Albeverio, S., & Danilov, V. (2012). Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics. Mathematische Nachrichten, 285(4), 426-439.
Albeverio, S., and Danilov, V. (2012). Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics. Mathematische Nachrichten 285, 426-439.
Albeverio, S., & Danilov, V., 2012. Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics. Mathematische Nachrichten, 285(4), p 426-439.
S. Albeverio and V. Danilov, “Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics”, Mathematische Nachrichten, vol. 285, 2012, pp. 426-439.
Albeverio, S., Danilov, V.: Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics. Mathematische Nachrichten. 285, 426-439 (2012).
Albeverio, Sergio, and Danilov, Vladimir. “Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics”. Mathematische Nachrichten 285.4 (2012): 426-439.
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