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We investigate the propagation of the slip front in the elastic body on therigid substrate. We first obtain the slip profile and the slip front velocityof the steady state by employing the local friction law with the quadratic formof the slip velocity and with vanishing static friction stress. The macroscopicstatic friction stress emerges spontaneously, which is expressed in terms ofthe parameter emerging in the friction law. For the model with viscosity, themacroscopic static friction stress again emerges spontaneously. The analyticaltreatment gives estimations for two slip front propagation velocities. Theycorresponds to two different boundary conditions, and one of them describes theframework employed here. Linear Marginal Stability Hypothesis based on thelinearized equation of motion shows that two slip front propagation velocitiesexist in this system, both of which coincide with the analytical solutionsnoted above. These imply that the linearized friction law dominantly governsthe slip front propagation behavior. Seismological implications are also givenbased on the analytical and numerical results.

Propagation velocity of slip front and emergence of macroscopic static friction in the system with vanishing local static friction