Existence and uniqueness theorems for the solution of an inverse problem for the transport equation
type: Item
instance of: scholarly article
title: Existence and uniqueness theorems for the solution of an inverse problem for the transport equation
zbMATH Open document ID: 0624.35079
DOI: 10.1007/BF00969996
author: A. Kh. Amirov
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The author studies some direct and inverse problems for the transport equation \[ u_ x \sin \phi +u_ y \cos \phi +u_{\phi}f=\lambda \] (u\(=u(x,y,\phi)\), \((x,y)\in D\subset {\mathbb{R}}^ 2\), \(\phi\in (0,2\pi))\), for example that of obtaining u and \(\lambda\) if f and the restriction of u to \(\partial D\times (0,2\pi)\) are given. Uniqueness theorems are proved by means of a priori estimates, existence theorems by a combination of regularization and Galerkin approximations. Here the two- and three-dimensional cases, however, require different techniques (e.g. different a priori estimates and choices of the function spaces involved).
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4013189
zbMATH Keywords: transport equation
zbMATH Keywords: Uniqueness
zbMATH Keywords: a priori estimates
zbMATH Keywords: existence
zbMATH Keywords: regularization
zbMATH Keywords: Galerkin approximations
reviewed by: Jürgen Appell
MaRDI profile type: Publication
cites work: Q5544877
cites work: Q4110032
cites work: Q5549989
cites work: Q3849114
cites work: Q5624013
description: scientific article; zbMATH DE number 4013189