In this paper we consider the optimal control of both operators and parameters for uncertain systems. For the optimal control and identification problem, we show existence of an optimal solution and present necessary conditions of optimality.

Advanced building design is a rather new interdisciplinary research branch, combining knowledge from physics, engineering, art and social science; its support from both theoretical and computational mathematics is needed. This paper shows an example of such collaboration, introducing a model problem of optimal heating in a low-energy house. Since all particular function values, needed for optimization are obtained as numerical solutions of an initial and boundary value problem for a sparse system...

For a class of infinite-dimensional minimization problems with nonlinear equality constraints, an iterative algorithm for finding global solutions is suggested. A key assumption is the convexity of the ''epigraph'', a set in the product of the image spaces of the constraint and objective functions. A convexification method involving randomization is used. The algorithm is based on the extremal shift control principle due to N.N. Krasovskii. An application to a problem of optimal control for a bilinear...

DiPerna's and Majda's generalization of Young measures is used to describe oscillations and concentrations in sequences of maps ${\left\{u_k\right\}}_{k\in \mathbb{N}}\subset L^p(\Omega ;{ℝ}^m)$ satisfying a linear differential constraint $𝒜u_k=0$. Applications to sequential weak lower semicontinuity of integral functionals on $𝒜$-free sequences and to weak continuity of determinants are given. In particular, we state necessary and sufficient conditions for weak* convergence of det$\nabla {\varphi }_k\stackrel{*}{\rightharpoonup }\det \nabla \varphi$ in measures on the closure of $\Omega \subset {ℝ}^n$ if ${\varphi }_k\rightharpoonup \varphi$ in $W^{1,n}(\Omega ;{ℝ}^n)$. This convergence holds, for example, under...

We use DiPerna’s and Majda’s generalization of Young measures to describe oscillations and concentrations in sequences of gradients, $\left\{\nabla u_k\right\}$, bounded in $L^p(Ø;{ℝ}^{m\times n})$ if $p\>1$ and $\Omega \subset {ℝ}^n$ is a bounded domain with the extension property in $W^{1,p}$. Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of $\Omega$ are required and links with lower semicontinuity results...

We use DiPerna's and Majda's generalization of Young measures to describe oscillations and concentrations in sequences of gradients, $\left\{\nabla u_k\right\}$, bounded in $L^p(\Omega ;{ℝ}^{m\times n})$ if p > 1 and $\Omega \subset {ℝ}^n$ is a bounded domain with the extension property in $W^{1,p}$. Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of Ω are required and links with lower semicontinuity...