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Bibliography

Journal Article

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

Rezunenko Oleksandr

: Journal of Abstract Differential Equations and Applications vol.2, 2 (2012), p. 56-71

: GAP103/12/2431, GA ČR

: partial differential equations, state-dependent delay, invariance principle

: http://library.utia.cas.cz/separaty/2012/AS/rezunenko- local properties of solutions to non-autonomous parabolic PDEs with state-dependent delays.pdf

(eng): 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.

: BC

2019-01-07 08:39