Approximation of semi-groups in the sense of Trotter and asymptotic mathematical modeling in physics of continuous media

Christian Licht (1, 2) , Thibaut Weller (1)

1 M3 - Mathématiques et Modélisations en Mécanique
2 Mahidol University [Bangkok]

We derive several models in Physics of continuous media using Trotter theory of convergence of semi-groups of operators acting on variable spaces.

Keywords: Asymptotic mathematical modeling; approximation of semi-groups in the sense of Trotter; transient problems; homogenization; reduction of dimension; Hilbert spaces of possible states with finite energy

Domains: Solid mechanics [physics.class-ph]

Christian Licht, Thibaut Weller. Approximation of semi-groups in the sense of Trotter and asymptotic mathematical modeling in physics of continuous media. Discrete and Continuous Dynamical Systems - Series S, 2019, 12 (6), pp.1709-1741. ⟨10.3934/dcdss.2019114⟩. ⟨hal-01951701⟩