Global in time solutions to Kolmogorov-Feller pseudodifferential equations with small parameter

S. Albeverio; V. G. Danilov

doi:10.1134/S1061920811010031

Global in time solutions to Kolmogorov-Feller pseudodifferential equations with small parameter

S. Albeverio^*, V. G. Danilov

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The goal in this paper is to demonstrate a new method for constructing globalin-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.

Original language	English
Pages (from-to)	10-25
Number of pages	16
Journal	Russian Journal of Mathematical Physics
Volume	18
Issue number	1
DOIs	https://doi.org/10.1134/S1061920811010031
State	Published - Mar 2011

Bibliographical note

Funding Information:
This work was supported by DFG project 436 RUS 113/895/0-1.

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1134/S1061920811010031

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title = "Global in time solutions to Kolmogorov-Feller pseudodifferential equations with small parameter",

abstract = "The goal in this paper is to demonstrate a new method for constructing globalin-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.",

author = "S. Albeverio and Danilov, \{V. G.\}",

note = "Funding Information: This work was supported by DFG project 436 RUS 113/895/0-1.",

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PY - 2011/3

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N2 - The goal in this paper is to demonstrate a new method for constructing globalin-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.

AB - The goal in this paper is to demonstrate a new method for constructing globalin-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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Global in time solutions to Kolmogorov-Feller pseudodifferential equations with small parameter

Abstract

Bibliographical note

ASJC Scopus subject areas

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