Abstract
The strength and stability of frictional interfaces, ranging from tribological systems to earthquake faults, are intimately related to the underlying spatially-extended dynamics. Here we provide a comprehensive theoretical account, both analytic and numeric, of spatiotemporal interfacial dynamics in a realistic rate-and-state friction model, featuring both velocity-weakening and strengthening behaviors. Slowly extending, loading-rate dependent, creep patches undergo a linear instability at a critical nucleation size, which is nearly independent of interfacial history, initial stress conditions and velocity-strengthening friction. Nonlinear propagating rupture fronts -- the outcome of instability -- depend sensitively on the stress state and velocity-strengthening friction. Rupture fronts span a wide range of propagation velocities and are related to steady state fronts solutions.
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