Non-linear partial differential equations with discrete state-dependent delays in a metric space

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Rezounenko, Alexander V.
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Abstract
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We investigate a class of non-linear partial differential equations with discrete state-dependent delays. The existence and uniqueness of strong solutions for initial functions from a Banach space are proved. To get the well-posed initial value problem we restrict our study to a smaller metric space, construct the dynamical system and prove the existence of a compact global attractor.
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Mathematics - Analysis of PDEs, Mathematics - Dynamical Systems, 35R10, 35B41, 35K57
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