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

0377979 - ÚTIA 2013 RIV US eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GAP103/12/2431
Institutional support: RVO:67985556
Keywords : partial differential equations * state-dependent delay * invariance principle
Subject RIV: BC - Control Systems Theory
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.
Permanent Link: http://hdl.handle.net/11104/0209980