The inverse problem of determining a source in the stationary transport equation for a Hamiltonian system
type: Item
instance of: scholarly article
title: The inverse problem of determining a source in the stationary transport equation for a Hamiltonian system
zbMATH Open document ID: 0884.58041
DOI: 10.1007/BF02104769
published in: Siberian Mathematical Journal
publication date: 1998-03-22T00:00:00Z
review text: The article is devoted to the problem, mentioned in its title, on manifolds. The main aim is to extend the author's previous existence results for Hamiltonians, quadratic in momentum variable, to Hamiltonians, which are convex and positively homogeneous in momentum. The consideration is based on some new deep constructions in the geometry of cotangent bundles. In particular, the author introduces the so-called bundle of semibasic tensors over a cotangent bundle and the so-called horizontal covariant derivative, playing a central role in the proof of results.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 53C05
zbMATH DE Number: 1023992
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: transport equation
zbMATH Keywords: covariant derivative
zbMATH Keywords: semibasic tensors
author: Vladimir Sharafutdinov
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
cites work: An inverse problem of determining a source in the stationary transport equation for a medium with refraction
cites work: The modified horizontal derivative and some of its applications
cites work: Q4756082
cites work: Q3663967
cites work: Q4003938
full work available at URL: https://doi.org/10.1007/bf02104769
OpenAlex ID: W2011557719
description: scientific article; zbMATH DE number 1023992