Approximation of semi-groups in the sense of Trotter and asymptotic mathematical modeling in physics of continuous media. (English) Zbl 1462.82030

Licht, Christian; Weller, Thibaut

Discrete Contin. Dyn. Syst., Ser. S 12, No. 6, 1709-1741 (2019).

The authors derive several models in Physics of continuous media using Trotter theory of convergence of semi-groups of operators acting on variable spaces. They consider the following examples which illustrate the necessity of considering variable spaces: i) gravity surface water waves; ii) more general water waves; iii) dynamics of linearly piezoelectric plates; iv) dynamics of two linearly elastic bodies connected by a thin an elastic layer.

Reviewer: Nasir N. Ganikhodjaev (Tashkent)

MSC:

82C21

Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics

Keywords:

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