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

Volume 2, Number 2 (2012), 56 - 71

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

Communicated By: 
Enrique Zuazua
Price: $20.00

Abstract

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, timedependent, 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.