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.
Revista:
Journal of Differential Equations

ISSN: 0022-0396

Any de publicació: 2017

Volum: 262

Número: 2

Pàgines: 1155-1160

Tipus: Article

DOI: 10.1016/J.JDE.2016.09.029 GOOGLE SCHOLAR lock_openAccés obert editor

Altres publicacions en: Journal of Differential Equations

Resum

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.

€ Mostra el finançament

Informació de finançament

Finançadors

Referències bibliogràfiques

  • 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