1,720,980 research outputs found
On homogenization of a mixed boundary optimal control problem
No full textWe study the asymptotic behaviour of an optimal control problem for the Ukawa equation in a thick multi-structure with different types and classes of admissible boundary controls. This thick
multi-structure consists of a domain (the junction's body) and a large number of "-periodically situated thin cylinders. We consider two types of boundary controls, namely, the Dirichlet H1/2-controls on the bases Ʈ ɛ of thin cylinders, and the Neumann L2-controls on their 'vertical'
sides. We present some ideas and results concerning of the asymptotic analysis for such problems as ɛ->0 and derive conditions under which the homogenized problem can be recovered in the explicit form. We show that the mathematical description of the homogenized optimal boundary
control problem is different from the original one. These differences appear not only in the control constraints, limit cost functional, state equations, and boundary conditions, but also in the type of admissible controls for the limit problem - one of them is the Dirichlet L2-control, whereas the second one is appeared as the distributed L2-control
On the Lavrentieff phenomenon in the homogenization of parabolic optimal control problems
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Boundary velocity suboptimal control of incompressible flow in cylindrically perforated domain
No full textIn this paper we study an optimal boundary control problem for the 3D steady-state Navier-Stokes equation in a cylindrically perforated domain Ωɛ The control is the boundary velocity field supported on the ‘vertical’ sides of thin cylinders. We minimize the vorticity of viscous flow through thick perforated domain. We show that an optimal solution to some limit problem in a non-perforated domain can be used as basis for the construction of suboptimal controls for the original control problem. It is worth noticing that the limit problem may take the form of either a variational calculation problem or an optimal control problem for Brinkman’s law with another cost
functional, depending on the cross-size of thin cylinders
On the Rate of Convergence of Solutions in Domain with Random Multilevel Oscillating Boundary
No full textIn the paper we deal with the homogenization problem for the Poisson equation in a singularly perturbed domain
with multilevel oscillating boundary. This domain consists of the body, a large number of thin periodically situated cylinders
joining to the body through thin random transmission zone with rapidly oscillating boundary. Inhomogeneous Fourier boundary
conditions with perturbed coefficients are set on the boundaries of the thin cylinders and on the boundary of the transmission
zone.We prove the homogenization theorems. Moreover we derive estimates of deviation of the solution to initial problem from
the solution to the homogenized problem in different cases.
It appears that depending on small parameters in Fourier boundary conditions of initial problem one can obtain Dirichlet,
Neumann or Fourier boundary conditions in the homogenized problem.We estimate the convergence of solutions in these three
cases
Asymptotic approximation for the solution to the Robin problem in a thick multi-level junction.
No full textWe consider a mixed boundary-value problem for the Poisson equation in a plane twolevel
junction Ωε, which is the union of a domain Ω0 and a large number 2N of thin
rods with variable thickness of order ε = O(N−1). The thin rods are divided into
two levels depending on their length. In addition, the thin rods from each level are
ε-periodically alternated. The Robin conditions are given on the lateral boundaries of
the thin rods. Using the method of matched asymptotic expansions, we construct the
asymptotic approximation for the solution as ε → 0 and prove the corresponding estimates
in the Sobolev space H1(Ωε)
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
On shape stability of Dirichlet optimal control problems in coefficients for nonlinear elliptic equations
No full textIn this paper we study a classical Dirichlet optimal control
problem for a nonlinear elliptic equation with the coefficients as controls
in L∞ (Ω). Since such problems have no solutions in general, we make
an assumption on the coefficients of the state equation and introduce
the class of so-called solenoidal controls. Using the direct method in the
calculus of variations, we prove the existence of at least one optimal pair.
We also study the stability of the above optimal control problem with
respect to the domain perturbation. With this goal we introduce the
concept of Mosco-stability for such problems and analyze the variational
properties of Mosco-stable problems with respect to different types of
domain perturbations
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