Shape optimization problems in control form

Multiphase Shape Optimization Problems

This paper is devoted to the analysis of multiphase shape optimization problems, which can formally be written as min { g ( (F1(Ω1), . . . , Fh(Ωh) ) +m ∣∣ h ⋃ i=1 Ωi ∣∣ : Ωi ⊂ D, Ωi ∩ Ωj = ∅}, where D ⊆ R is a given bounded open set, |Ωi| is the Lebesgue measure of Ωi and m is a positive constant. For a large class of such functionals, we analyse qualitative properties of the cells and the int...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Variational Methods in Shape Optimization Problems

It's not surprisingly when entering this site to get the book. One of the popular books now is the variational methods in shape optimization problems. You may be confused because you can't find the book in the book store around your city. Commonly, the popular book will be sold quickly. And when you have found the store to buy the book, it will be so hurt when you run out of it. This is why, se...

Optimization Problems in Congestion Control

One of the crucial elements in the Internet’s success is its ability to adequately control congestion. This paper defines and solves several optimization problems related to Internet congestion control, as a step toward understanding the virtues of the TCP congestion control algorithm currently used and comparing it with alternative algorithms. We focus on regulating the rate of a single unicas...

Shape Optimization for Dynamic Contact Problems

The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost ...