Markov decision models (MDM) used in practical applications are most often less complex than the underlying ‘true’ MDM. The reduction of model complexity is performed for several reasons. However, it is obviously of interest to know what kind of model reduction is reasonable (in regard to...

Optimal control problems for a class of 1D semilinear parabolic equations with cubic nonlinearity are considered. This class is also known as the Schlögl model. Main emphasis is laid on the control of traveling wave fronts that appear as typical solutions to the state equation. The...

In this work linear-quadratic optimal control problems for parabolic equations with mixed control-state constraints are considered. These problems arise when a Lavrentiev regularization is utilized for state constrained linear-quadratic optimal control problems. For the numerical solution a...

Three results are presented: First, we solve the problem of persistence of dissipation for reduction of kinetic models. Kinetic equations with thermodynamic Lyapunov functions are studied. Uniqueness of the thermodynamic projector is proven: There exists only one projector which transforms any...

In this paper, we construct low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A...

The combination of spatial smoothing and asymptotic analysis allows reduction of computationally expensive 3D fuel cell models to 2D without sacrificing leading-order physics. This paper investigates, demonstrates, and verifies the spatial smoothing and asymptotic reduction of a 3D...

Dynamical low-rank approximation is a differential-equation-based approach to efficiently compute low-rank approximations to time-dependent large data matrices or to solutions of large matrix differential equations. We illustrate its use in the following application areas: as an updating...