Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions

摘要

Partial differential equations with discrete (concentrated) state-dependentdelays in the space of continuous functions are investigated. In general, thecorresponding initial value problem is not well posed, so we find an additionalassumption on the state-dependent delay function to guarantee the wellposedness. For the constructed dynamical system we study the long-timeasymptotic behavior and prove the existence of a compact global attractor.