Optimal Starting-Stopping Problems for Markov-Feller Processes

By means of nested inequalities in semigroup form we give a characterization of the value functions of the starting-stopping problem for general Markov-Feller processes. Next, we consider two versions of constrained problems on the nal state or on the final time. The plan is as follows: Introduction Nested variational inequalities Solution of optimal starting-stopping problem Problems with constraints References

Order reduction methods for solving large-scale differential matrix Riccati equations

We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen as a promising class of solution strategies, by forming low-rank approximations to the sought after solution at selected timesteps. We show that great computational and memory savings are obtained by a reduction process onto rational Krylov subspaces, as opposed to current approaches. By specifically addressing the solution of the reduced differential equation and reliable stopping criteria, we are able to obtain accurate final approximations at low memory and computational requirements. This is obtained by employing a two-phase strategy that separately enhances the accuracy of the algebraic approximation and the time integration. The new method allows us to numerically solve much larger problems than in the current literature. Numerical experiments on benchmark problems illustrate the effectiveness of the procedure with respect to existing solvers

Recovery of a space-dependent vector source in thermoelastic systems

In this contribution, an inverse problem of determining a space-dependent vector source in a thermoelastic system of type-I, type-II and type-III is studied using information from a supplementary measurement at a fixed time. These thermoelastic systems consist of two equations that are coupled: a parabolic equation for the temperature [GRAPHICS] and a vectorial hyperbolic equation for the displacement [GRAPHICS] . In this latter one, the source is unknown, but solely space dependent. A spacewise-dependent additional measurement at the final time ensures that the inverse problem corresponding with each type of thermoelasticity has a unique solution when a damping term [GRAPHICS] (with [GRAPHICS] componentwise strictly monotone increasing) is present in the hyperbolic equation. Despite the ill-posed nature of these inverse problems, a stable iterative algorithm is proposed to recover the unknown source in the case that [GRAPHICS] is also linear. This method is based on a sequence of well-posed direct problems, which are numerically solved at each iteration, step by step, using the finite element method. The instability of the inverse source problem is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results support the theoretically obtained results