Local Properties of Solutions to Non-Autonomous Parabolic PDEs with State-Dependent Delays

0377979 - ÚTIA 2013 RIV US eng J - Článek v odborném periodiku
Rezunenko, Oleksandr
Local Properties of Solutions to Non-Autonomous Parabolic PDEs with State-Dependent Delays.
Journal of Abstract Differential Equations and Applications. Roč. 2, č. 2 (2012), s. 56-71. ISSN 2158-611X
Grant CEP: GA ČR(CZ) GAP103/12/2431
Institucionální podpora: RVO:67985556
Klíčová slova: partial differential equations * state-dependent delay * invariance principle
Kód oboru RIV: BC - Teorie a systémy řízení
http://library.utia.cas.cz/separaty/2012/AS/rezunenko- local properties of solutions to non-autonomous parabolic PDEs with state-dependent delays.pdf

A wide class of non-autonomous nonlinear parabolic partial differential equations with delay is studied. We allow in our investigations different types of delays such as constant, time- dependent, state-dependent (both discrete and distributed) to be presented simultaneously. The main difficulties arise due to the presence of discrete state-dependent delays since the nonlinear delay term is not Lipschitz on the space of continuous functions. We find conditions for the local existence, uniqueness and study the invariance principle.
Trvalý link: http://hdl.handle.net/11104/0209980