Hyperbolic Equations with Unknown Coefficients

Hyperbolic Equations with Unknown Coefficients

We study the solvability of nonlinear inverse problems of determining the low order coefficients in the second order hyperbolic equation. The overdetermination condition is specified as an integral condition with final data. Existence and uniqueness theorems for regular solutions are proved (i.e. fo...

Full description

Bibliographic Details
Main Author: Aleksandr I. Kozhanov
Format: Article
Language:English
Published: MDPI AG 2020-09-01
Series:Symmetry
Subjects:
hyperbolic equation
inverse problem
unknown coefficient
final-integral overdetermination condition
regular solution
existence
Online Access:https://www.mdpi.com/2073-8994/12/9/1539
id doaj-ebd0b5a2043146fc8c91dbd2902431ad
record_format Article
spelling doaj-ebd0b5a2043146fc8c91dbd2902431ad2020-11-25T03:43:48ZengMDPI AGSymmetry2073-89942020-09-01121539153910.3390/sym12091539Hyperbolic Equations with Unknown CoefficientsAleksandr I. Kozhanov0Sobolev Institute of Mathematics, Acad. Koptyug av. 4, 630090 Novosibirsk, RussiaWe study the solvability of nonlinear inverse problems of determining the low order coefficients in the second order hyperbolic equation. The overdetermination condition is specified as an integral condition with final data. Existence and uniqueness theorems for regular solutions are proved (i.e. for solutions having all weak derivatives in the sense of Sobolev, occuring in the equation).https://www.mdpi.com/2073-8994/12/9/1539hyperbolic equationinverse problemunknown coefficientfinal-integral overdetermination conditionregular solutionexistence
collection DOAJ
language English
format Article
sources DOAJ
author Aleksandr I. Kozhanov
spellingShingle Aleksandr I. Kozhanov
Hyperbolic Equations with Unknown Coefficients
Symmetry
hyperbolic equation
inverse problem
unknown coefficient
final-integral overdetermination condition
regular solution
existence
author_facet Aleksandr I. Kozhanov
author_sort Aleksandr I. Kozhanov
title Hyperbolic Equations with Unknown Coefficients
title_short Hyperbolic Equations with Unknown Coefficients
title_full Hyperbolic Equations with Unknown Coefficients
title_fullStr Hyperbolic Equations with Unknown Coefficients
title_full_unstemmed Hyperbolic Equations with Unknown Coefficients
title_sort hyperbolic equations with unknown coefficients
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2020-09-01
description We study the solvability of nonlinear inverse problems of determining the low order coefficients in the second order hyperbolic equation. The overdetermination condition is specified as an integral condition with final data. Existence and uniqueness theorems for regular solutions are proved (i.e. for solutions having all weak derivatives in the sense of Sobolev, occuring in the equation).
topic hyperbolic equation
inverse problem
unknown coefficient
final-integral overdetermination condition
regular solution
existence
url https://www.mdpi.com/2073-8994/12/9/1539
work_keys_str_mv AT aleksandrikozhanov hyperbolicequationswithunknowncoefficients
_version_ 1724518238887346176

Similar Items