Online Analysis and PDE seminar (UAM-UC-UC3M-UCM-ICMAT-IMUS)

**Online Analysis and PDE seminar**(UAM-UC-UC3M-UCM-ICMAT-IMUS)

**Conferenciante:** Maria Eugenia Pérez, Universidad de Cantabria

**Fecha:** Miércoles 15 de junio de 2022 - 15:00

**Resumen:**We consider a spectral homogenization problem for the elasticity operator posed in a bounded domain of the upper half-space, a part of its boundary being in contact with the plane. We assume that this surface is free outside small regions in which we impose Robin-Winkler boundary conditions linking stresses and displacements by means of a symmetric and positive definite matrix and a reaction parameter. These small regions are periodically placed along the plane while its size is much smaller than the period. We provide all the possible spectral homogenized problems depending on certain asymptotic relations between the period, the size of the regions and the reaction-parameter. We show the convergence of the eigenelements, as the period tends to zero, which deeply involves the corresponding microscopic stationary problems obtained by means of asymptotic expansions.

**Referencias:**

[1] D. Gómez, S.A. Nazarov, ; M.-E. Pérez-Martínez. Asymptotics for spectral problems with rapidly alternating boundary conditions on a strainer Winkler foundation. Journal of Elasticity, 2020, V. 142, p. 89-120.

[2] D. Gómez, S.A. Nazarov ; M.-E. Pérez-Martínez. Spectral homogenization problems in linear elasticity with large reaction terms concentrated in small regions of the boundary. In: Computational and Analytic Methods in Science and Engineering. Birkäuser, Springer, N.Y., 2020, pp. 121-143

[3] M.-E. Pérez-Martínez. Homogenization for alternating boundary conditions with large reaction terms concentrated in small regions. In: Emerging problems in the homogenization of Partial Differential Equations. ICIAM2019 SEMA SIMAI Springer Series 10, 2021, pp. 37-57.

[2] D. Gómez, S.A. Nazarov ; M.-E. Pérez-Martínez. Spectral homogenization problems in linear elasticity with large reaction terms concentrated in small regions of the boundary. In: Computational and Analytic Methods in Science and Engineering. Birkäuser, Springer, N.Y., 2020, pp. 121-143

[3] M.-E. Pérez-Martínez. Homogenization for alternating boundary conditions with large reaction terms concentrated in small regions. In: Emerging problems in the homogenization of Partial Differential Equations. ICIAM2019 SEMA SIMAI Springer Series 10, 2021, pp. 37-57.

Location Fecha: Miércoles 15 de junio de 2022 - 15:00