Non-local PDEs with discrete state-dependent delays: well-posedness in a metric space

Details Non-local PDEs with discrete state-dependent delays: well-posedness in a metric space Non-local PDEs with discrete state-dependent delays: well-posedness in a metric space

2010-11-10

arxiv.org/abs/1011.2444v1

Mathematics

Analysis of PDEs

Scientific paper

Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of continuously differentiable (with respect to an appropriate norm) functions is used to construct a dynamical system. This subset is an analogue of \textit{the solution manifold} proposed for ordinary equations in [H.-O. Walther, The solution manifold and $C\sp 1$-smoothness for differential equations with state-dependent delay, J. Differential Equations, {195}(1), (2003) 46--65]. The existence of a compact global attractor is proven.

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