Roland Schnaubelt

Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line

AbstractLetU=(U(t, s))t≥s≥O be an evolution family on the half-line of bounded linear operators on a Banach spaceX. We introduce operatorsGO,GX andIX on certain spaces ofX-valued continuous functions connected with the integral equation

Functional analytic methods for evolution equations

u(t) = U(t,s)u(s) + \int_s^t {U(t,\xi )f(\xi )d\xi }

Well-posedness and Asymptotic Behaviour of Non-autonomous Linear Evolution Equations

, and we characterize exponential stability, exponential expansiveness and exponential dichotomy ofU by properties ofGO,GX andIX, respectively. This extends related results known for finite dimensional spaces and for evolution families on the whole line, respectively.

Asymptotic Behaviour of Parabolic Nonautonomous Evolution Equations

We prove that the exponential dichotomy of a strongly continuous evolution family on a Banach space is equivalent to the existence and uniqueness of continuous bounded mild solutions of the corresponding inhomogeneous equation. This result addresses nonautonomous abstract Cauchy problems with unbounded coefficients. The technique used involves evolution semigroups. Some applications are given to evolution families on scales of Banach spaces arising in center manifolds theory.

Lp-Theory for Elliptic Operators on R^d with Singular Coefficients

Preface.- Giuseppe Da Prato: An Introduction to Markov Semigroups.- Peer C. Kunstmann and Lutz Weis: Maximal

Two classes of passive time-varying well-posed linear systems

L_p -regularity for Parabolic Equations, Fourier Multiplier Theorems and

Parabolic evolution equations with asymptotically autonomous delay

H^\infty

Convergence of an ADI splitting for Maxwell's equations

-functional Calculus.- Irena Lasiecka: Optimal Control Problems and Riccati Equations for Systems with Unbounded Controls and Partially Analytic Generators-Applications to Boundary and Point Control Problems.- Alessandra Lunardi: An Introduction to Parabolic Moving Boundary Problems.- Roland Schnaubelt: Asymptotic Behaviour of Parabolic Nonautonomous Evolution Equations.