Asymptotic analysis and scaling of friction parameters |
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Authors: | Dorin Bucur Ioan R Ionescu |
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Institution: | (1) Laboratoire de Mathématiques, Université de Metz, Ile du Saulcy, 57045 Metz, France;(2) Laboratoire de Mathématiques, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac, France |
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Abstract: | We consider an eigenvalue problem associated to the antiplane shearing on a system of collinear faults under a slip-dependent
friction law. Firstly we consider a periodic system of faults in the whole plane. We prove that the first eigenvalues/eigenfunctions
of different physical periodicity are all equal and that the other eigenvalues converge to this first common eigenvalue as
their physical period becomes indefinitely large. Secondly we consider a large scale fault system composed on a small scale
collinear faults periodically disposed. If β0* is the first eigenvalue of the periodic problem in the whole plane, we prove that the first eigenvalue of the microscopic
problem behaves as β0*/∈ when ∈→ 0 regardless the geometry of the domain (here ∈ is the scale quotient). The geophysical implications of this result
is that the macroscopic critical slip Dc scales with Dc∈/∈ (here Dc∈ is the small scale critical slip). |
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Keywords: | 35P15 35P20 49R50 86A15 |
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