Naslov
Homogenization of the time-dependent heat equation on planar one-dimensional periodic structures

Autori
Ljulj, Matko ; Schmidt, Kersten ; Semin, Adrien ; Tambača, Josip

Izvornik
Applicable analysis (0003-6811) 101 (2022), 12; 4046-4075

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
80M40 ; 35R02 ; 2-scale convergence ; thin structures ; energies ; respect models

Sažetak
In this paper we consider the homogenization of a time-dependent heat conduction problem on a planar one-dimensional periodic structure. On the edges of a graph the one-dimensional heat equation is posed, while the Kirchhoff junction condition is applied at all (inner) vertices. Using the two-scale convergence adapted to homogenization of lower-dimensional problems we obtain the limit homogenized problem defined on a two-dimensional domain that is occupied by the mesh when the mesh period δ tends to 0. The homogenized model is given by the classical heat equation with the conductivity tensor depending on the unit cell graph only through the topology of the graph and lengthes of its edges. We show the well-posedness of the limit problem and give a purely algebraic formula for the computation of the homogenized conductivity tensor. The analysis is completed by numerical experiments showing a convergence to the limit problem where the convergence order in δ depends on the unit cell pattern.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA