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:
Introduction Read chapter Read first chapter

2013 | OriginalPaper | Chapter

3. Essential and Absolute Spectra

Authors : Todd Kapitula, Keith Promislow

Published in: Spectral and Dynamical Stability of Nonlinear Waves

Publisher: Springer New York

Log in

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

search-config
loading …

Abstract

The goal of this chapter is the characterization of the essential spectrum and Fredholm indices of two classes of linear differential operators on unbounded domains. The first class is comprised of nth-order differential operators with spatially varying coefficients that tend at an exponential rate to constant values at \(\pm \infty \).

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 Background Material and Notation
next chapter Asymptotic Stability of Waves in Dissipative Systems
Literature
[30]
A. Ben-Artzi and I. Gohberg. Dichotomy of systems and invertibility of linear ordinary differential operators. Operator Theory Adv. Appl., 56: 91–119, 1992.
[53]
C. Chicone and Y. Latushkin. Evolution Semigroups in Dynamical Systems and Differential Equations, volume 70 of Math. Surv. Monogr. American Mathematical Society, Providence, RI, 1999.
[59]
W.A. Coppel. Dichotomies in stability theory. In Lecture Notes in Mathematics 629. Springer-Verlag, New York, 1978.
[65]
J. Daleckii and M. Krein. Stability of Solutions of Differential Equations in Banach Space, volume 43 of Trans. Math. Monogr. American Mathematical Society, Providence, RI, 1974.
[82]
B. Fiedler and A. Scheel. Spatio-Temporal Dynamics of Reaction–Diffusion Patterns, Trends in Nonlinear Analysis. Springer-Verlag, Berlin, 2003.
[112]
J. Hale. Ordinary Differential Equations. Robert E. Krieger Publishing, Malabar, FL, second edition, 1980.MATH
[113]
J. Härterich, B. Sandstede, and A. Scheel. Exponential dichotomies for linear non-autonomous functional differential equations of mixed type. Indiana U. Math. J., 51:1081–1109, 2002.MATHCrossRef
[182]
[200]
W. Magnus and S. Winkler. Hill’s Equation, volume 20 of Interscience Tracts in Pure and Applied Mathematics. Interscience, New York, 1966.
[215]
[216]
[221]
[239]
J. Rademacher, B. Sandstede, and A. Scheel. Computing absolute and essential spectra using continuation. Physica D, 229(1&2):166–183, 2007.MathSciNetMATHCrossRef
[242]
M. Reed and B. Simon. Methods of Modern Mathematical Physics IV: Analysis of Operators. Academic Press, New York, 1978.MATH
[250]
B. Sandstede. Stability of travelling waves. In Handbook of Dynamical Systems, volume 2, chapter 18, pp. 983–1055. Elsevier, New York, 2002.
[252]
B. Sandstede and A. Scheel. Absolute and convective instabilities of waves on unbounded and large bounded domains. Physica D, 145:233–277, 2000a.MathSciNetMATHCrossRef
[255]
[257]
B. Sandstede and A. Scheel. Relative Morse indices, Fredholm indices, and group velocities. Disc. Cont. Dyn. Syst., 20:139–158, 2008.MathSciNetMATH
Metadata
Title
Essential and Absolute Spectra
Authors
Todd Kapitula
Keith Promislow
Copyright Year
2013
Publisher
Springer New York
Book
Spectral and Dynamical Stability of Nonlinear Waves

Print ISBN: 978-1-4614-6994-0

Electronic ISBN: 978-1-4614-6995-7

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-6995-7_3