Unspecified Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: http://doi.org/10.5167/uzh-22758 Originally published at: Chipot, M; Fila, M; Quittner, P (1991). Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions. Acta Mathematica Universitatis Comenianae. New Series, 60(1):35-1...

We consider boundary value problems for semilinear evolution inclusions. We establish the existence of extremal solutions. Using that result, we show that the evolution inclusion has periodic extremal trajectories. These results are then applied to closed loop control systems. Finally, an example of a semilinear parabolic distributed parameter control system is worked out in detail.

We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strateg...

In this paper an observability analysis is performed for an axial dispersion tubular bioreactor that involves one nonlinear growth reaction. The process is described by a semilinear parabolic Partial Differential Equation (PDE). More precisely, the analysis is performed on a tangent linearized model, that is described by a linear PDE with a spatial-dependent coefficient. It is reported that the...

A formula for the transition density of a Markov process defined by an infinite-dimensional stochastic equation is given in terms of the Ornstein–Uhlenbeck bridge and a useful lower estimate on the density is provided. As a consequence, uniform exponential ergodicity and V ergodicity are proved for a large class of equations. We also provide computable bounds on the convergence rates and the sp...

A formula for the transition density of a Markov process defined by an infinitedimensional stochastic equation is given in terms of the Ornstein Uhlenbeck Bridge, and a useful lower estimate on the density is provided. As a consequence, uniform exponential ergodicity and V-ergodicity are proven under suitable conditions for a large class of equations. The method allows us to find computable bou...