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.
Non-local PDEs with discrete state-dependent delays: well-posedness in a metric space
A condition on delay for differential equations with discrete state-dependent delay
Non-local PDEs with a state-dependent delay term presented by Stieltjes integral
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