Please use this identifier to cite or link to this item:
http://hdl.handle.net/10077/16207
Title: | Smoothness issues in differential equations with state-dependent delay | Authors: | Krisztin, Tibor Walther, Hans-Otto |
Keywords: | Delay differential equation; state-dependent delay; solution manifold; stable manifold; solution operator; smoothness; mollification; threshold delay | Issue Date: | 2017 | Publisher: | EUT Edizioni Università di Trieste | Source: | Tibor Krisztin, Hans-Otto Walther, "Smoothness issues in differential equations with state-dependent delay"in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics", 49 (2017), Trieste, EUT Edizioni Università di Trieste, 2017, pp. 95-112 | Journal: | Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics | Part of: | 49 (2017) | Abstract: | For differential equations with state-dependent delays a satisfactory theory is developed by the second author [6] on the solution manifold to guarantee C1 -smoothness for the solution operators. We present examples showing that better than C1 -smoothness cannot be expected in general for the solution manifold and for local stable manifolds at stationary points on the solution manifold. Then we propose a new approach to overcome the diffi culties caused by the lack of smoothness. The mollification technique is used to approximate the nonsmooth evaluation map with smooth maps. Several examples show that the mollified systems can have nicer smoothness properties than the original equation. Examples are also given where better smoothness than C1 can be obtained on the solution manifold. |
Type: | Article | URI: | http://hdl.handle.net/10077/16207 | ISSN: | 0049-4704 | eISSN: | 2464-8728 | DOI: | 10.13137/2464-8728/16207 | Rights: | Attribution-NonCommercial-NoDerivatives 4.0 Internazionale |
Appears in Collections: | Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol.49 (2017) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
07_RIMUT_TiborHans.pdf | 348.5 kB | Adobe PDF | ![]() View/Open |
CORE Recommender
Page view(s)
126
Last Week
1
1
Last month
checked on Nov 23, 2019
Download(s)
69
checked on Nov 23, 2019
Google ScholarTM
Check
Altmetric
This item is licensed under a Creative Commons License