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Mathematical models of seismics in composite media: elastic and poro-elastic components. (English) Zbl 1349.35025

Electron. J. Differ. Equ. 2016, Paper No. 184, 22 p. (2016); addendum ibid. 2016, Paper No. 184, p. 22 (2016).
Summary: In the present paper we consider elastic and poroelastic media having a common interface. We derive the macroscopic mathematical models for seismic wave propagation through these two different media as a homogenization of the exact mathematical model at the microscopic level. They consist of seismic equations for each component and boundary conditions at the common interface, which separates different media. To do this we use the two-scale expansion method in the corresponding integral identities, defining the weak solution. We illustrate our results with the numerical implementations of the inverse problem for the simplest model.
Editorial remark: A big portion of this paper coincides verbatim with the paper [the authors and S. T. Mukhambetzhanov, Sib. Élektron. Mat. Izv. 13, 75–88 (2016; Zbl 1349.35024)] which is not cited in the list of references.
There is an addendum at the end of the paper referring to the duplication.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
86A15 Seismology (including tsunami modeling), earthquakes
86A22 Inverse problems in geophysics

Citations:

Zbl 1349.35024
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