Addendum to “Travelling waves for a non-local Korteweg–de Vries–Burgers equation” [J. Differential Equations 257 (3) (2014) 720–758]

  1. Cuesta, C.M.
  2. Achleitner, F.
Zeitschrift:
Journal of Differential Equations

ISSN: 0022-0396

Datum der Publikation: 2017

Ausgabe: 262

Nummer: 2

Seiten: 1155-1160

Art: Artikel

DOI: 10.1016/J.JDE.2016.09.029 GOOGLE SCHOLAR lock_openOpen Access editor

Andere Publikationen in: Journal of Differential Equations

Zusammenfassung

We add a theorem to F. Achleitner, C.M. Cuesta and S. Hittmeir (2014) [1]. In that paper we studied travelling wave solutions of a Korteweg–de Vries–Burgers type equation with a non-local diffusion term. In particular, the proof of existence and uniqueness of these waves relies on the assumption that the exponentially decaying functions are the only bounded solutions of the linearised equation. In this addendum we prove this assumption and thus close the existence and uniqueness proof of travelling wave solutions.

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Bibliographische Referenzen

  • Achleitner, (2014), J. Differential Equations, 257, pp. 720, 10.1016/j.jde.2014.04.015
  • Achleitner, (2011), J. Differential Equations, 250, pp. 2177, 10.1016/j.jde.2010.11.015
  • Kilbas, (2006), vol. 204
  • Kreĭn, (1958), Uspekhi Mat. Nauk, 13, pp. 3
  • Lieb, (1997), vol. 14
  • Wiener, (1931), Sitz.ber. Preuss. Akad. Wiss. Berl., XXXI, pp. 696