Viscosity solutions for dynamic problems with slip-rate dependent friction

Dynamic Contact with Signorini’s Condition and Slip Rate Dependent Friction

Existence of a weak solution for the problem of dynamic frictional contact between a viscoelastic body and a rigid foundation is established. Contact is modelled with the Signorini condition. Friction is described by a slip rate dependent friction coefficient and a nonlocal and regularized contact stress. The existence in the case of a friction coefficient that is a graph, which describes the j...

Dynamic Contact Problems with Slip-dependent Friction in Viscoelasticity

The dynamic evolution with frictional contact of a viscoelastic body is considered. The assumptions on the functions used in modelling the contact are broad enough to include both the normal compliance and the Tresca models. The friction law uses a friction coefficient which is a non-monotone function of the slip. The existence and uniqueness of the solution are proved in the general three-dime...

Dynamic scaling in stick-slip friction

Stochastic Target Problems, Dynamic Programming, and Viscosity Solutions

In this paper, we de ne and study a new class of optimal stochastic control problems which is closely related to the theory of Backward SDE's and forward-backward SDE's. The controlled process (X ; Y ) takes values in IRd IR and a given initial data for X (0). Then, the control problem is to nd the minimal initial data for Y so that it reaches a stochastic target at a speci ed terminal time T ....

Self-similar slip instability on interfaces with rate- and state-dependent friction.

We examine the development of a frictional instability, with diverging sliding rate, at the interface of elastic bodies in contact. Evolution of friction is determined by a slip rate and state dependence. Following Viesca (2016 Phys. Rev. E93, 060202(R). (doi:10.1103/PhysRevE.93.060202)), we show through an appropriate change of variable, the existence of blow-up solutions that are fixed points...