Analysis of dynamic ruptures generating seismic waves in a self-gravitating planet: An iterative coupling scheme and well-posedness

de Hoop, Maarten; Kumar, Kundan; Ye, Ruichao

doi:10.1090/qam/1561

Online ISSN 1552-4485; Print ISSN 0033-569X

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Analysis of dynamic ruptures generating seismic waves in a self-gravitating planet: An iterative coupling scheme and well-posedness

Authors: Maarten V. de Hoop, Kundan Kumar and Ruichao Ye
Journal: Quart. Appl. Math. 78 (2020), 485-511
MSC (2010): Primary 76D05, 35K86, 76D03, 35A35, 49J40
DOI: https://doi.org/10.1090/qam/1561
Published electronically: November 25, 2019
MathSciNet review: 4100290
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the solution of the system of equations describing the dynamical evolution of spontaneous ruptures generated in a prestressed elastic-gravitational deforming body and governed by rate and state friction laws. We propose an iterative coupling scheme based on a weak formulation with nonlinear interior boundary conditions, both for continuous time and with implicit discretization (backward Euler) in time. We regularize the problem by introducing viscosity. This guarantees the convergence of the scheme for solutions of the regularized problems in both cases. We also make precise the conditions on the relevant coefficients for convergence to hold.

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