Method of reflections applied to the construction of the asymptotics of Green's function for parabolic equations with variable coefficients
type: Item
instance of: scholarly article
title: Method of reflections applied to the construction of the asymptotics of Green's function for parabolic equations with variable coefficients
zbMATH Open document ID: 0884.35023
DOI: 10.1007/BF02303981
author: Yanyan Li
published in: Mathematical Notes
publication date: 1996-02-21T00:00:00Z
review text: A method for constructing the asymptotic representation of Green's function for the equation \[ -h {\partial G\over \partial t} +H\left( {\overset {2} x}, -h{\overset {1} {{\partial \over \partial x}}} \right) G=0, \quad x\geq 0 \tag{1} \] as \(h\to 0\) is presented. Here, the Hamiltonian \(H(x,p)\) of equation (1) is an analytic function in \(p\), infinitely differentiable in \(x\) and real-valued for real values of the arguments, and satisfies for \((x,p,\eta) \in\mathbb{R}_+ \times \mathbb{R} \times \mathbb{R}\) the conditions \(\partial^2 H(x,p)/\partial p^2>0\), \(\text{Re} H(x,p+i \eta) \leq H(x,p)\). The symbols \({\overset {2} x}\), \(\overset {1}{{\partial \over \partial x}}\), are as introduced by \textit{V. P. Maslov} [Operational methods, Moscow, Mir (1976; Zbl 0449.47002)]. The method is based on a particular representation of the \(\delta\)-function obtained by the first author.
reviewed by: Vojislav Marić
Mathematics Subject Classification ID: 35C20
zbMATH DE Number: 846507
zbMATH Keywords: Green's function
MaRDI profile type: Publication
cites work: Q3973446
full work available at URL: https://doi.org/10.1007/bf02303981
OpenAlex ID: W2002502736
description: scientific article; zbMATH DE number 846507