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 β *0 is the first eigenvalue of the periodic problem in the whole plane, we prove that the first eigenvalue of the microscopic problem behaves as β *0 /∈ 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 D c scales with D ∈ c /∈ (here D ∈ c is the small scale critical slip).
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Bucur, D., Ionescu, I.R. Asymptotic analysis and scaling of friction parameters. Z. angew. Math. Phys. 57, 1042–1056 (2006). https://doi.org/10.1007/s00033-006-0070-9
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DOI: https://doi.org/10.1007/s00033-006-0070-9