Parabolic partial differential equations with discrete state-dependent delay: Classical solutions and solution manifold

By Tibor Krisztin, A. Rezounenko. 2014

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Abstract Classical solutions to PDEs with discrete state-dependent delay are studied. We prove the well-posedness in a set X F which is 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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2a0190a99fab8f32ae715bfbc5c3f3dfe367abdf