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

2009/04/15 by Alexander V. Rezounenko, Rezounenko, Alexander V.
Mathematics · #35B41 #35K57 #35R10 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AP #math.DS #msc:35B41 #msc:35K57 #msc:35R10

paper · pdf · doi:10.48550/arxiv.0904.2308

arxiv created 2009/04/15 · arxiv updated 2009/12/01

Abstract

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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