Local Properties of Solutions to Non-Autonomous Parabolic PDEs with State-Dependent Delays
Result description
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 ?nd conditions for the local existence, uniqueness and study the invariance principle.
Keywords
partial differential equationsstate-dependent delayinvariance principle
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Local Properties of Solutions to Non-Autonomous Parabolic PDEs with State-Dependent Delays
Original language description
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 ?nd conditions for the local existence, uniqueness and study the invariance principle.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BC - Theory and management systems
OECD FORD branch
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Result continuities
Project
GAP103/12/2431: Systems described by partial differential equations with delays
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Abstract Differential Equations and Applications
ISSN
2158-611X
e-ISSN
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Volume of the periodical
2
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
56-71
UT code for WoS article
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EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BC - Theory and management systems
Year of implementation
2012