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

0457879 - ÚTIA 2017 RIV US eng J - Journal Article
Krisztin, T. - Rezunenko, Oleksandr
Parabolic partial differential equations with discrete state-dependent delay: Classical solutions and solution manifold.
Journal of Differential Equations. Roč. 260, č. 5 (2016), s. 4454-4472. ISSN 0022-0396. E-ISSN 1090-2732
R&D Projects: GA ČR GAP103/12/2431
Institutional support: RVO:67985556
Keywords : Parabolic partial differential equations * State dependent delay * Solution manifold
Subject RIV: BC - Control Systems Theory
Impact factor: 1.988, year: 2016
http://library.utia.cas.cz/separaty/2016/AS/rezunenko-0457879.pdf

Classical solutions to PDEs with discrete state-dependent delay are studied. We prove the well-posedness in a set XF which is analogous to the solution manifold used for ordinary differential equations with statedependent delay. We prove that the evolution operators are C1-smooth on the solution manifold.
Permanent Link: http://hdl.handle.net/11104/0258401