Differentiability with respect to (t,s) of the parabolic evolution operator (Q910935)

The author investigates the differentiability with respect to (t,s) of the evolution operator G(t,s) associated with a time-dependent family of generators of analytic semigroups \(\{\) A(t)\(\}\) in a Banach space, having constant (but not necessarily dense) domain, and analyzes the singularity of the derivatives of G(t,s) as t approaches s. The abstract results are applied to derive representation formulae for the solution of strictly parabolic initial-boundary value problems having non-homogeneous boundary values of Dirichlet or of regular oblique derivative type.