Parabolic partial differential equations with state-dependent delays (SDDs) are investigated. The delay term presented by Stieltjes integral simultaneously includes discrete and distributed SDDs. The singular Lebesgue-Stieltjes measure is also admissible. The conditions for the corresponding initial value problem to be well-posed are presented. The existence of a compact global attractor is proved.
A condition on delay for differential equations with discrete state-dependent delay
Parabolic partial differential equations with discrete state-dependent delay: classical solutions and solution manifold
Non-local PDEs with discrete state-dependent delays: well-posedness in a metric space
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