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Title (deu)
Homogenisation of nonlinear Dirichlet problems in randomly perforated domains
Speaker / Lecturer
Caterina Zeppieri
WWU Münster
Description (deu)

This talk was part of the Workshop on "New perspective on Shape and Topology Optimization" held at the ESI December 11 — 15, 2023.

We study the convergence of integral functionals with q-growth in an n-dimensional bounded domain, with n>q>1, which is perforated by a random number of small spherical holes with random radii and centres. Assuming that the latter are generated by a stationary short-range marked point process, we show that in the small-perforations limit we obtain an averaged nonlinear analogue of the capacitary term obtained by Cioranescu and Murat in the linear deterministic periodic case. We only require that the random radii have finite (n-q)-moment, which is the minimal assumption to ensure that the expectation of the nonlinear q-capacity of the spherical holes is finite. Although under this assumption there are holes which overlap with probability one, we show that the clustering holes do not have any impact on the homogenisation procedure.

Keywords (deu)
Mathematicsmetamaterialstopology optimizationshape optimization
Subject (eng)
ÖFOS 2012 -- 1010 -- Mathematics
Type (eng)
Language
[eng]
Persistent identifier
https://phaidra.univie.ac.at/o:2041840
Date created
2023-12-14
Place of creation (eng)
ESI
Duration
44 minutes 50 seconds
Content
Details
Object type
Video
Format
video/mp4
Created
11.01.2024 11:30:48
Metadata