Non-local PDEs with a state-dependent delay term presented by Stieltjes integral

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.