Existence of classical solutions for parabolic functional differential equations with initial boundary conditions of Robin type
Tom 105 / 2012
Annales Polonici Mathematici 105 (2012), 253-265 MSC: Primary 35K20; Secondary 35R10. DOI: 10.4064/ap105-3-4
The paper deals with the initial boundary value problem of Robin type for parabolic functional differential equations. The unknown function is the functional variable in the equation and the partial derivatives appear in the classical sense. A theorem on the existence of a classical solution is proved. Our formulation and results cover differential equations with deviated variables and differential integral problems.