Eugenio Sinestrari

Cα-regularity for non-autonomous linear integrodifferential equations of parabolic type

Abstract Linear integrodifferential equations in general Banach space are studied and applications are given to linear integrodifferential partial differential equations.

Non autonomous evolution operators of hyperbolic type

In this paper we consider a Cauchy problem in a Banach spaceE:u′(t)=A(t)u(t)+f(t), t∈[t0, T], u(t0)=u0, whereA(·) is a family of linear operators inE which satisfy all the requirements of Katos semigroup approach to the non autonomous hyperbolic equations except for the density of the common domains ofA(t). An application is given to a hyperbolic partial differential equation with discontinuous coefficients.

Abstract Hyperbolic Equations in Non-reflexive Spaces

Let X be a Banach space and A: D(A) ⊂ X →X a linear operator and consider homogeneous linear abstract Cauchy problem:.