New approach to streaming semigroups with dissipative boundary conditions.
New approach to streaming semigroups with multiplying boundary conditions.
New characterizations of asymptotic stability for evolution families on Banach spaces.
New classes of analytic and Gevrey semigroups and applications
We consider the operator on a complex Hilbert space, where is positive self-adjoint and is self-adjoint, and where, moreover, « is comparable to , », in a technical sense. Two applications are given.
New spectral criteria for almost periodic solutions of evolution equations
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...
Non autonomous evolution operators of hyperbolic type.
Non-autonomous inhomogeneous boundary Cauchy problems.
Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour.
Non-autonomous stochastic Cauchy problems in Banach spaces
We study the non-autonomous stochastic Cauchy problem on a real Banach space E, , t ∈ [0,T], U(0) = u₀. Here, is a cylindrical Brownian motion on a real separable Hilbert space H, are closed and densely defined operators from a constant domain (B) ⊂ H into E, denotes the generator of an evolution family on E, and u₀ ∈ E. In the first part, we study existence of weak and mild solutions by methods of van Neerven and Weis. Then we use a well-known factorisation method in the setting of evolution...
Norm continuity of -semigroups
We show that a positive semigroup on with generator A and ||R(α + i β)|| → 0 as |β| → ∞ for some α ∈ ℝ is continuous in the operator norm for t>0. The proof is based on a criterion for norm continuity in terms of “smoothing properties” of certain convolution operators on general Banach spaces and an extrapolation result for the -scale, which may be of independent interest.
Norms for copulas.
Notes on Analytic Convoluted -semigroups
Notes on the propagators of evolution equations.
Numerical exponential decay to dissipative Bresse system.