Global in Time Solutions to Kolmogorov-Feller Pseudodifferential Equations with Small Parameter

Details Global in Time Solutions to Kolmogorov-Feller Pseudodifferential Equations with Small Parameter Global in Time Solutions to Kolmogorov-Feller Pseudodifferential Equations with Small Parameter

2011-01-31

arxiv.org/abs/1101.5836v1

Physics

Mathematical Physics

27 pages

Scientific paper

The goal in this paper is to demonstrate a new method for constructing global-in-time approximate (asymptotic) solutions of (pseudodifferential) parabolic equations with a small parameter. We show that, in the leading term, such a solution can be constructed by using characteristics, more precisely, by using solutions of the corresponding Hamiltonian system and without using any integral representation. For completeness, we also briefly describe the well-known scheme developed by V.P.Maslov for constructing global-in-time solutions.

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