Addendum to “Travelling waves for a non-local Korteweg–de Vries–Burgers equation” [J. Differential Equations 257 (3) (2014) 720–758]
- Cuesta, C.M.
- Achleitner, F.
ISSN: 0022-0396
Year of publication: 2017
Volume: 262
Issue: 2
Pages: 1155-1160
Type: Article
More publications in: Journal of Differential Equations
Abstract
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.
Funding information
Funders
- Vienna University of Technology
-
MINECO
- MTM2014-53145-P
-
Basque Government
- IT641-13
Bibliographic References
- 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