Computation and Stability of Traveling Waves in Second Order Evolution Equations

Beyn W-J, Otten D, Rottmann-Matthes J (2018)
SIAM Journal on Numerical Analysis 56(3): 1786-1817.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Autor/in
Abstract / Bemerkung
The topic of this paper is nonlinear traveling waves occuring in a system of damped wave equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this method generates a co-moving frame in which the solution becomes stationary. In addition, it generates an algebraic variable which converges to the speed of the wave, provided the original wave satisfies certain spectral conditions and initial perturbations are sufficiently small. We develop a rigorous theory for this effect by recourse to some recent nonlinear stability results for waves in first order hyperbolic systems. Numerical computations illustrate the theory for examples of Nagumo and FitzHugh-Nagumo type.
Stichworte
systems of damped wave equations; traveling waves; nonlinear stability; freezing method; second order evolution equations; point spectra; essential spectra
Erscheinungsjahr
2018
Zeitschriftentitel
SIAM Journal on Numerical Analysis
Band
56
Ausgabe
3
Seite(n)
1786-1817
ISSN
0036-1429
eISSN
1095-7170
Page URI
https://pub.uni-bielefeld.de/record/2921249

Zitieren

Beyn W-J, Otten D, Rottmann-Matthes J. Computation and Stability of Traveling Waves in Second Order Evolution Equations. SIAM Journal on Numerical Analysis. 2018;56(3):1786-1817.
Beyn, W. - J., Otten, D., & Rottmann-Matthes, J. (2018). Computation and Stability of Traveling Waves in Second Order Evolution Equations. SIAM Journal on Numerical Analysis, 56(3), 1786-1817. doi:10.1137/16M108286X
Beyn, W. - J., Otten, D., and Rottmann-Matthes, J. (2018). Computation and Stability of Traveling Waves in Second Order Evolution Equations. SIAM Journal on Numerical Analysis 56, 1786-1817.
Beyn, W.-J., Otten, D., & Rottmann-Matthes, J., 2018. Computation and Stability of Traveling Waves in Second Order Evolution Equations. SIAM Journal on Numerical Analysis, 56(3), p 1786-1817.
W.-J. Beyn, D. Otten, and J. Rottmann-Matthes, “Computation and Stability of Traveling Waves in Second Order Evolution Equations”, SIAM Journal on Numerical Analysis, vol. 56, 2018, pp. 1786-1817.
Beyn, W.-J., Otten, D., Rottmann-Matthes, J.: Computation and Stability of Traveling Waves in Second Order Evolution Equations. SIAM Journal on Numerical Analysis. 56, 1786-1817 (2018).
Beyn, Wolf-Jürgen, Otten, Denny, and Rottmann-Matthes, J. “Computation and Stability of Traveling Waves in Second Order Evolution Equations”. SIAM Journal on Numerical Analysis 56.3 (2018): 1786-1817.