Construction of the fundamental solution of disturbed parabolic equation
type: Item
instance of: scholarly article
title: Construction of the fundamental solution of disturbed parabolic equation
zbMATH Open document ID: 1029.58017
DOI: 10.1016/S0007-4497(03)00006-X
author: Victor Bondarenko
published in: Bulletin des Sciences Mathématiques
publication date: 2003-09-15T00:00:00Z
review text: In the present work the problem of construction of a fundamental solution \(e^{t(L+L_1)}\) of the equation \(u_t=(L+L_1)u\) is considered. The operators \(L\) and \(L_1\) are elliptic ones and the properties of the evolution operator \(e^{tL}\) of a non-disturbed equation \(u_t=L u\) are assumed to be known. The construction is reduced to an iterative procedure the convergence of which is proved. Two examples of perturbed parabolic equations are considered.
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 35K10
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 1981553
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: heat kernel
zbMATH Keywords: curvature tensor
reviewed by: Lubomira Softova
MaRDI profile type: Publication
cites work: Diffusion sur une variété de courbure non positive
cites work: q-Numbers of quantum groups, Fibonacci numbers, and orthogonal polynomials
cites work: Parametrix method for a parabolic equation on a Riemannian manifold
cites work: The logarithmic gradient of the heat kernel on a Riemannian manifold.
cites work: Théoremes de comparaison en géométrie Riemannienne
cites work: On the heat kernel of a complete Riemannian manifold
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description: scientific article; zbMATH DE number 1981553