Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
An Inverse Conductivity Problem in Multifrequency Electric Impedance Tomography Read chapter Read first chapter

2020 | OriginalPaper | Chapter

7. Carleman Estimate for a General Second-Order Hyperbolic Equation

Author : Xinchi Huang

Published in: Inverse Problems and Related Topics

Publisher: Springer Singapore

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this article, we consider a general second-order hyperbolic equation. We first establish a modified Carleman estimate for this equation by adding some functions of adjustment. Then general conditions imposed on the principal parts, mixed with the weight function and the functions of adjustment are derived. Finally, we give the realizations of the weight functions by choosing suitable adjustments such that the above general conditions are satisfied in some specific cases.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Inverse Problems for a Compressible Fluid System
next chapter A Priori Parameter Choice in Tikhonov Regularization with Oversmoothing Penalty for Non-linear Ill-Posed Problems
Literature
1.
A. Amirov, M. Yamamoto, A timelike Cauchy problem and an inverse problem for general hyperbolic equations. Appl. Math. Lett. 21, 885–891 (2008)MathSciNetCrossRef
2.
M. Bellassoued, M. Yamamoto, Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems (Springer-Japan, Tokyo, 2017)CrossRef
3.
O.Yu. Imanuvilov, On Carleman estimates for hyperbolic equations. Asymptot. Anal. 32, 185–220 (2002)
4.
V. Isakov, Inverse Problems for Partial Differential Equations (Springer, Berlin, 2006)MATH
5.
V. Isakov, N. Kim, Weak Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress. Appl. Math. 27(2), 799–825 (2010)MathSciNetMATH
6.
O.Yu. Imanuvilov, M. Yamamoto, Global uniqueness and stability in determining coefficients of wave equations. Comm. Part. Differ. Equ. 26, 1409–1425 (2001)
7.
M.V. Klibanov, A. Timonov, Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (VSP, Utrecht, 2004)CrossRef
8.
I. Lasiecka, R. Triggiani, P. Yao, Inverse/observability estimates for second-order hyperbolic equations with variable coefficients. J. Math. Anal. Appl. 235, 13–57 (1999)MathSciNetCrossRef
9.
R. Triggiani, P. Yao, Carleman estimates with no lower-order terms for general riemann wave equations. global uniqueness and observability in one shot. Appl. Math. Optim. 46, 331–375 (2002)
10.
Metadata
Title
Carleman Estimate for a General Second-Order Hyperbolic Equation
Author
Xinchi Huang
Copyright Year
2020
Publisher
Springer Singapore
Book
Inverse Problems and Related Topics

Print ISBN: 978-981-15-1591-0

Electronic ISBN: 978-981-15-1592-7

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-981-15-1592-7_7

Premium Partner

    Image Credits