Justification of the exact asymptotics of the fundamental solution for a degenerate parabolic equation with a small parameter
type: Item
instance of: scholarly article
title: Justification of the exact asymptotics of the fundamental solution for a degenerate parabolic equation with a small parameter
zbMATH Open document ID: 1547.35408
author: V. G. Danilov
author: Mark Rakhel
published in: ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
publication date: 2024-05-21T00:00:00Z
review text: In this paper, the authors discuss the asymptotics of the fundamental solution of a linear degenerate parabolic equation with a small parameter. Using the operator representation of the Dirac delta function and the WKB method, they construct the asymptotic expansion with respect to the small parameter (i.e., the WKB expansion) of the fundamental solution for a class of linear degenerate parabolic equations. They also show that for this class of degenerate parabolic equations the WKB expansion of the fundamental solution converges, which immediately justifies the asymptotics of the WKB expansion.
reviewed by: Yoshitsugu Takei
Mathematics Subject Classification ID: 35K08
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 7851229
zbMATH Keywords: Wentzel-Kramers-Brillouin (WKB) method
MaRDI profile type: Publication
cites work: The Fundamental Solution to the Wright–Fisher Equation
cites work: The fundamental solution to 1D degenerate diffusion equation with one-sided boundary
cites work: Fundamental solution to 1D degenerate diffusion equation with locally bounded coefficients
cites work: Q4040558
cites work: Q3682920
cites work: DIFFUSION PROCESSES AND RIEMANNIAN GEOMETRY
cites work: Q5798359
cites work: Q3896271
cites work: ON SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS
cites work: Tunnel canonical operator in thermodynamics
cites work: A representation of the delta function via creation operators and Gaussian exponentials, and multiplicative fundamental solution asymptotics for some parabolic pseudodifferential equations
cites work: Development of Maslov's approach to the construction of nonoscillating WKB-type solutions
DOI: 10.1002/ZAMM.202300491
description: scientific article; zbMATH DE number 7851229