2023-11-30T02:21:46Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/726592023-08-25T16:50:59Zcom_20.500.14352_14col_20.500.14352_15
A strange non-local monotone operator arising in the homogenization of a diffusion equatio with dynamic nonlinear boundary conditions on particles of critical size and arbitrary shape
Díaz Díaz, Jesús Ildefonso
Shaposhnikova, Tatiana
Zubova, Maria N.
We characterize the homogenization limit of the solution of a Poisson equation in a bounded domain, either periodically perforated or containing a set of asymmetric periodical small particles and on the boundaries of these particles a nonlinear dynamic boundary condition holds involving a Hölder nonlinear [sigma](u). We consider the case in which the diameter of the perforations (or the diameter of particles) is critical in terms of the period of the structure. As in many other cases concerning critical size, a "strange" nonlinear term arises in the homogenized equation. For this case of asymmetric critical particles we prove that the effective equation is a semilinear elliptic equation in which the time arises as a parameter and the nonlinear expression is given in terms of a nonlocal operator H which is monotone and Lipschitz continuous on L2(0;T), independently of the regularity of [sigma].
2023-06-22T12:29:22Z
2023-06-22T12:29:22Z
2022-07-18
journal article
1072-6691
https://hdl.handle.net/20.500.14352/72659
https://ejde.math.txstate.edu/
eng
PID2020-112517GB-I00
UCM Research Group MOMAT (ref. 910480)
https://creativecommons.org/licenses/by/3.0/es/
open access
Atribución 3.0 España