Analysis of dynamic ruptures generating seismic waves in a self-gravitating planet: an iterative coupling scheme and well-posedness. (English) Zbl 1435.76022
Summary: 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.
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35K86 | Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 35A35 | Theoretical approximation in context of PDEs |
| 49J40 | Variational inequalities |
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