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Local Properties of Solutions to Non-Autonomous Parabolic PDEs with State-Dependent Delays
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SYSNO ASEP 0377979 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Ostatní články Title Local Properties of Solutions to Non-Autonomous Parabolic PDEs with State-Dependent Delays Author(s) Rezunenko, Oleksandr (UTIA-B) RID Number of authors 1 Source Title Journal of Abstract Differential Equations and Applications - ISSN 2158-611X
Roč. 2, č. 2 (2012), s. 56-71Number of pages 16 s. Language eng - English Country US - United States Keywords partial differential equations ; state-dependent delay ; invariance principle Subject RIV BC - Control Systems Theory R&D Projects GAP103/12/2431 GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2013
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