It has been shown recently that steady frictional sliding along an interfac
e between dissimilar elastic solids with Coulomb friction acting at the int
erface is ill-posed for a wide range of material parameters and friction co
efficients. The ill-posedness is manifest in the unstable growth of interfa
cial disturbances of all wavelengths, with growth rate inversely proportion
al to the wavelength. We first establish the connection between the ill-pos
edness and the existence of a certain interfacial wave in frictionless cont
act, called the generalized Rayleigh wave. Precisely, it is shown that for
material combinations where the generalized Rayleigh wave exists, steady sl
iding with Coulomb friction is ill-posed for arbitrarily small values of fr
iction. Tn addition, intersonic unstable modes and supersonic steady-state
modes exist for sufficiently large values of the friction coefficient. Seco
ndly, regularization of the problem by an experimentally motivated friction
law is studied. We show that a friction law with no instantaneous dependen
ce on normal stress but a simple fading memory of prior history of normal s
tress makes the problem well-posed. (C) 2001 Published by Elsevier Science
Ltd.