Optimal Shape for Elliptic Problems with Random Perturbations

Details Optimal Shape for Elliptic Problems with Random Perturbations Optimal Shape for Elliptic Problems with Random Perturbations

2010-02-14

arxiv.org/abs/1002.2770v1

Mathematics

Optimization and Control

17 pages, 6 figures

Scientific paper

In this paper we analyze the relaxed form of a shape optimization problem with state equation $\{{array}{ll} -div \big(a(x)Du\big)=f\qquad\hbox{in}D \hbox{boundary conditions on}\partial D. {array}.$ The new fact is that the term $f$ is only known up to a random perturbation $\xi(x,\omega)$. The goal is to find an optimal coefficient $a(x)$, fulfilling the usual constraints $\alpha\le a\le\beta$ and $\displaystyle\int_D a(x) dx\le m$, which minimizes a cost function of the form $$\int_\Omega\int_Dj\big(x,\omega,u_a(x,\omega)\big) dx dP(\omega).$$ Some numerical examples are shown in the last section, to stress the difference with respect to the case with no perturbation.

Affiliated with

Also associated with

No associations

Rating

Optimal Shape for Elliptic Problems with Random Perturbations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Optimal Shape for Elliptic Problems with Random Perturbations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal Shape for Elliptic Problems with Random Perturbations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-555070