Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Analysis of a dislocation model for earthquakes


Authors: Jing Liu, Xin Yang Lu and Noel J. Walkington
Journal: Quart. Appl. Math. 74 (2016), 765-786
MSC (2010): Primary 86A17, 74S05, 49J45
DOI: https://doi.org/10.1090/qam/1445
Published electronically: July 21, 2016
MathSciNet review: 3539031
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Abstract: Approximation of problems in linear elasticity having small shear modulus in a thin region is considered. Problems of this type arise when modeling ground motion due to earthquakes where rupture occurs in a thin fault. It is shown that, under appropriate scaling, solutions of these problems can be approximated by solutions of a limit problem where the fault region is represented by a surface. In a numerical context this eliminates the need to resolve the large deformations in the fault; a numerical example is presented to illustrate efficacy of this strategy.


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Additional Information

Jing Liu
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Email: jingliu1@andrew.cmu.edu

Xin Yang Lu
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Canada
Email: xinyang.lu@mcgill.ca

Noel J. Walkington
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Email: noelw@andrew.cmu.edu

DOI: https://doi.org/10.1090/qam/1445
Received by editor(s): April 21, 2016
Published electronically: July 21, 2016
Additional Notes: The third author was supported in part by National Science Foundation grants DMS–1418991 and DMREF–1434734. This work was also supported by the NSF through the Center for Nonlinear Analysis.
Article copyright: © Copyright 2016 Brown University


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