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Numerical Functional Analysis and Optimization Volume 20, 1999 - Issue 3-4
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Original Articles

Stability of traveling waves: dichotomies and eigenvalue conditions on finite intervals

Wolf-Jürgen Beyn Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, Bielefeld, 33501
&
Jens Lorenz Department of Mathematics and Statistics, UNM, Albuquerque, NM, 87131
Pages 201-244 | Published online: 15 May 2007

Citations (40)

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Read on this site (3)

Oksana Guba. (2009) Using Root Functions for Eigenvalue Problems of Ordinary Differential Operators. Numerical Functional Analysis and Optimization 30:11-12, pages 1289-1308.
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Wolf-Jürgen Beyn & Jens Rottmann-Matthes. (2007) Resolvent Estimates for Boundary Value Problems on Large Intervals Via the Theory of Discrete Approximations. Numerical Functional Analysis and Optimization 28:5-6, pages 603-629.
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Peter L Simon, Serafim Kalliadasis, John H Merkin & Stephen K Scott. (2003) Evans function analysis of the stability of non-adiabatic flames. Combustion Theory and Modelling 7:3, pages 545-561.
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Articles from other publishers (37)

Peter Howard. (2021) Hörmander's index and oscillation theory. Journal of Mathematical Analysis and Applications 500:1, pages 125076.
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M. Beck, G. Cox, C. Jones, Y. Latushkin, K. McQuighan & A. Sukhtayev. (2018) Instability of pulses in gradient reaction–diffusion systems: a symplectic approach. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376:2117, pages 20170187.
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W.-J. Beyn, D. Otten & J. Rottmann-Matthes. (2018) Computation and Stability of Traveling Waves in Second Order Evolution Equations. SIAM Journal on Numerical Analysis 56:3, pages 1786-1817.
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Wolf-Jürgen Beyn, Yuri Latushkin & Jens Rottmann-Matthes. (2013) Finding Eigenvalues of Holomorphic Fredholm Operator Pencils Using Boundary Value Problems and Contour Integrals. Integral Equations and Operator Theory 78:2, pages 155-211.
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Jonathan A. Sherratt, Ayawoa S. Dagbovie & Frank M. Hilker. (2013) A Mathematical Biologist’s Guide to Absolute and Convective Instability. Bulletin of Mathematical Biology 76:1, pages 1-26.
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Ravi P. Agarwal, Claudio Cuevas & Carlos LizamaRavi P. Agarwal, Claudio Cuevas & Carlos Lizama. 2014. Regularity of Difference Equations on Banach Spaces. Regularity of Difference Equations on Banach Spaces 119 197 .
Wolf-Jürgen Beyn, Luca Dieci, Nicola Guglielmi, Ernst Hairer, Jesús María Sanz-Serna & Marino ZennaroWolf-Jürgen Beyn, Denny Otten & Jens Rottmann-Matthes. 2014. Current Challenges in Stability Issues for Numerical Differential Equations. Current Challenges in Stability Issues for Numerical Differential Equations 89 172 .
Xiao-Biao Lin. (2013) Stability of standing waves for monostable reaction?convection equations in a large bounded domain with boundary conditions. Journal of Differential Equations 255:1, pages 58-84.
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Todd Kapitula & Keith PromislowTodd Kapitula & Keith Promislow. 2013. Spectral and Dynamical Stability of Nonlinear Waves. Spectral and Dynamical Stability of Nonlinear Waves 249 304 .
Yuri Latushkin & Alim Sukhtayev. (2012) The Evans function and the Weyl-Titchmarsh function. Discrete and Continuous Dynamical Systems - Series S 5:5, pages 939-970.
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Je-Chiang Tsai, Wenjun Zhang, Vivien Kirk & James Sneyd. (2012) Traveling Waves in a Simplified Model of Calcium Dynamics. SIAM Journal on Applied Dynamical Systems 11:4, pages 1149-1199.
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Oksana Guba & Jens Lorenz. (2011) Continuous spectra and numerical eigenvalues. Mathematical and Computer Modelling 54:11-12, pages 2616-2622.
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Luca Dieci, Cinzia Elia & Erik Van Vleck. (2011) Detecting exponential dichotomy on the real line: SVD and QR algorithms. BIT Numerical Mathematics 51:3, pages 555-579.
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Jens Rottmann-Matthes. (2011) Linear Stability of Traveling Waves in First-Order Hyperbolic PDEs. Journal of Dynamics and Differential Equations 23:2, pages 365-393.
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Weishi Liu & Erik S. Van Vleck. (2010) Exponential Dichotomy for Asymptotically Hyperbolic Two-Dimensional Linear Systems. Journal of Dynamics and Differential Equations 22:4, pages 697-722.
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Margaret Beck, Zhenguo Pan & Brian Wetton. (2010) Stability of travelling wave solutions for coupled surface and grain boundary motion. Physica D: Nonlinear Phenomena 239:17, pages 1730-1740.
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Luca Dieci, Cinzia Elia & Erik Van Vleck. (2010) Exponential dichotomy on the real line: SVD and QR methods. Journal of Differential Equations 248:2, pages 287-308.
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Oksana Guba. (2009) Convergence of Green’s functions of ordinary differential equations. Mathematical and Computer Modelling 50:3-4, pages 542-555.
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V. Thümmler. (2007) The Effect of Freezing and Discretization to the Asymptotic Stability of Relative Equilibria. Journal of Dynamics and Differential Equations 20:2, pages 425-477.
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Vera Thümmler. (2008) Numerical Approximation of Relative Equilibria for Equivariant PDEs. SIAM Journal on Numerical Analysis 46:6, pages 2978-3005.
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Peter L. Simon. 2008. Large-Scale Scientific Computing. Large-Scale Scientific Computing 217 224 .
J. Rottmann-Matthes. 2008. Hyperbolic Problems: Theory, Numerics, Applications. Hyperbolic Problems: Theory, Numerics, Applications 901 909 .
Gunilla Kreiss, Heinz-Otto Kreiss & Jens Lorenz. (2007) Stability of Viscous Shocks on Finite Intervals. Archive for Rational Mechanics and Analysis 187:1, pages 157-183.
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Claudio Cuevas & Claudio vidal. (2006) A note on discrete maximal regularity for functional difference equations with infinite delay. Advances in Difference Equations 2006, pages 1-12.
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Wolf-Jürgen Beyn & Jens Lorenz. (2006) Stability of Viscous Profiles: Proofs Via Dichotomies. Journal of Dynamics and Differential Equations 18:1, pages 141-195.
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Yongkui Zou & Wolf-Jürgen Beyn. (2004) On the existence of transversal heteroclinic orbits in discretized dynamical systems. Nonlinearity 17:6, pages 2275-2292.
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Y.-K. Zou & W.-J. Beyn. (2003) On manifolds of connecting orbits in discretizations of dynamical systems. Nonlinear Analysis: Theory, Methods & Applications 52:5, pages 1499-1520.
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Thomas J. Bridges, Gianne Derks & Georg Gottwald. (2002) Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework. Physica D: Nonlinear Phenomena 172:1-4, pages 190-216.
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Björn Sandstede. 2002. 983 1055 .
A. Afendikov & A. Mielke. (2001) Nonlocal modulation equations for viscous-fluid flows in layers and spatially localized perturbations. Doklady Physics 46:12, pages 869-872.
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Björn Sandstede & Arnd Scheel. (2001) On the Structure of Spectra of Modulated Travelling Waves. Mathematische Nachrichten 232:1, pages 39-93.
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Andrei L Afendikov & Thomas J Bridges. (2001) Instability of the Hocking-Stewartson pulse and its implications for three-dimensional Poiseuille flow. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 457:2006, pages 257-272.
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Wolf-Jürgen Beyn, Winfried Kleß & Vera Thümmler. 2001. Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems. Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems 47 72 .
Alexander Mielke, Guido Schneider & Hannes Uecker. 2001. Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems. Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems 563 583 .
Gunilla Kreiss & Mattias Liefvendahl. 2001. Hyperbolic Problems: Theory, Numerics, Applications. Hyperbolic Problems: Theory, Numerics, Applications 613 621 .
Björn Sandstede & Arnd Scheel. (2000) Absolute and convective instabilities of waves on unbounded and large bounded domains. Physica D: Nonlinear Phenomena 145:3-4, pages 233-277.
Crossref
Gabriel J. Lord, Daniela Peterhof, Björn Sandstede & Arnd Scheel. (2000) Numerical Computation of Solitary Waves in Infinite Cylindrical Domains. SIAM Journal on Numerical Analysis 37:5, pages 1420-1454.
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