Parabolic partial differential equations with discrete state-dependent delay: classical solutions and solution manifold (1412.0219v1)

Abstract: Classical solutions to PDEs with discrete state-dependent delay are studied. We prove the well-posedness in a set $X_F$ which is an analogous to the solution manifold used for ordinary differential equations with state-dependent delay. We prove that the evolution operators are $C^1$-smooth on the solution manifold.