In this paper, we consider a domain Ω(ε)⊂RN, N≥2, with a very rough boundary depending on ε. For instance, if N=3 Ω(ε) has the form of a brush with an ε-periodic distribution of thin cylindrical teeth with fixed height and a small diameter of order ε. In Ω(ε) we consider a nonlinear monotone problem with nonlinear Signorini boundary conditions, depending on ε on the lateral boundary of the teeth. We study the asymptotic behavior of this problem, as ε vanishes, i.e. when the number of thin attached cylinders increases unboundedly, while their cross sections tend to zero. We identify the limit problem which is a nonstandard homogenized problem. Namely, in the region filled up by the thin cylinders the limit problem is given by a variational inequality coupled to an algebraic system.

Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary

Antonio Gaudiello;
2018

Abstract

In this paper, we consider a domain Ω(ε)⊂RN, N≥2, with a very rough boundary depending on ε. For instance, if N=3 Ω(ε) has the form of a brush with an ε-periodic distribution of thin cylindrical teeth with fixed height and a small diameter of order ε. In Ω(ε) we consider a nonlinear monotone problem with nonlinear Signorini boundary conditions, depending on ε on the lateral boundary of the teeth. We study the asymptotic behavior of this problem, as ε vanishes, i.e. when the number of thin attached cylinders increases unboundedly, while their cross sections tend to zero. We identify the limit problem which is a nonstandard homogenized problem. Namely, in the region filled up by the thin cylinders the limit problem is given by a variational inequality coupled to an algebraic system.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/740115
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