Non-local PDEs with discrete state-dependent delays: well-posedness in a metric space
Analysis of PDEs
2010-11-11 v1 Dynamical Systems
Abstract
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 -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.
Keywords
Cite
@article{arxiv.1011.2444,
title = {Non-local PDEs with discrete state-dependent delays: well-posedness in a metric space},
author = {Alexander V. Rezounenko and Petr Zagalak},
journal= {arXiv preprint arXiv:1011.2444},
year = {2010}
}