András Bátkai

Operator splitting for non-autonomous evolution equations

Abstract We establish general product formulas for the solutions of non-autonomous abstract Cauchy problems. The main technical tools are evolution semigroups allowing the direct application of existing results on autonomous problems. The results obtained are illustrated by the example of an autonomous diffusion equation perturbed with time dependent potential. We also prove convergence rates for the sequential splitting applied to this problem.

Differential equation approximations of stochastic network processes: an operator semigroup approach

The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs that depends on the state space size (

Operator splittings and spatial approximations for evolution equations

N

Decomposition of operator semigroups on W*-algebras

) and can be written as

Cosine families generated by second-order differential operators on W1,1(0, 1) with generalized Wentzell boundary conditions

\dot u_N=A_N u_N

Operator Splitting with Spatial-temporal Discretization

. Our results rely on the convergence of the transition matrices

Operator splitting for nonautonomous delay equations

A_N

Hyperbolicity of linear partial differential equations with delay

to an operator

The norm convergence of a Magnus expansion method

A

On the Effect of Small Delays to the Stability of Feedback Systems

. This convergence also implies that the solutions