Parabolic partial differential equations with discrete state-dependent delay: Classical solutions and solution manifold

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Krisztin, Tibor¹  Rezounenko, Alexander^2,3 

[1] Univ Szeged, Bolyai Inst, MTA SZTE Anal & Stochast Res Grp, Aradi Vertanuk Tere 1, H-6720 Szeged, Hungary

[2] Kharkov Natl Univ, UA-61022 Kharkov, Ukraine

[3] AS CR, Inst Informat Theory & Automat, POB 18, Prague 18208, Czech Republic

关键词: Parabolic partial differential equations;    State dependent delay;    Solution manifold;   

DOI  :  10.1016/j.jde.2015.11.018

来源: Elsevier

【 摘 要 】

Classical solutions to PDEs with discrete state-dependent delay are studied. We prove the well-posedness in a set X-F which is analogous to the solution manifold used for ordinary differential equations with state dependent delay. We prove that the evolution operators are C-1-smooth on the solution manifold. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free