Local properties of solutions to non-autonomous parabolic PDEs with state-dependent delays

Details Local properties of solutions to non-autonomous parabolic PDEs with state-dependent delays Local properties of solutions to non-autonomous parabolic PDEs with state-dependent delays

2011-04-06

arxiv.org/abs/1104.1125v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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.

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