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.
Revue:
Journal of Differential Equations

ISSN: 0022-0396

Année de publication: 2017

Volumen: 262

Número: 2

Pages: 1155-1160

Type: Article

DOI: 10.1016/J.JDE.2016.09.029 GOOGLE SCHOLAR lock_openAccès ouvert editor

D'autres publications dans: Journal of Differential Equations

Résumé

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.

€ Voir financement

Information sur le financement

Financeurs

Références bibliographiques

  • 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