In this paper is presented the problem of optimizing a functional over a Pareto control set associated with a convex multiobjective control problem in Hilbert spaces, namely parabolic system. This approach generalizes for this setting some results obtained in finite dimensions. Some examples are presented. General optimality results are obtained, and a special attention is paid to the linear-qu...

Talk Abstract We describe the application of arbitrary-order Hermite methods to hyperbolic-parabolic systems, including parabolic systems as a special case, emphasizing situations where the parabolic terms are small (e.g. large Reynolds or Peclet numbers). Using Fourier methods, we study the dispersion relation for the semidiscretized problem, leading to an understanding of time-step stability ...

In this paper we derive W1,∞ and piecewise C1,α estimates for solutions, and their t−derivatives, of divergence form parabolic systems with coefficients piecewise Hölder continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of...

We consider the tracking problem for parabolic systems with boundary control. Assuming that the reference signal is bounded and measurable, we prove various regularity results as well representation formulas for the optimal control and the optimal trajectory.

We consider an elliptic PDE in two variables. As one parameter approaches zero, this PDE collapses to a parabolic one, that is forward parabolic in a part of the domain and backward parabolic in the remainder. Such problems arise naturally in various stochastic models, such as fluid models for data-handling systems and Markov-modulated queues. We employ singular perturbation methods to study th...

In the first part of this paper, we study abstract parabolic evolution equations involving Banach space-valued measures. These results are applied in the second part to second-order parabolic systems under minimal regularity hypotheses on the coefficients. DOI: https://doi.org/10.1007/s10958-005-0376-8 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi....

We consider an elliptic PDE in two variables. As one parameter approaches zero, this PDE collapses to a parabolic one, that is forward parabolic in a part of the domain and backward parabolic in the remainder. Such problems arise naturally in various stochastic models, such as fluid models for data-handling systems and Markovmodulated queues. We employ singular perturbation methods to study the...