$w(x,t)$	horizontal component of displacements in the coating
${\mathsf{\sigma }}_{xx}(x,t)$	normal component of stresses in the coating
${\mathsf{\sigma }}_{xy}(x,t)$	shear component of stresses in the coating
$T(x,t)$	the coating temperature
$h$	thickness of the coating
$V$	sliding velocity of the abrasive (half-plane I)
$\mathsf{\mu }(x)$	shear modulus of the coating material
$\mathsf{\nu }$	Poisson’s ratio of the coating material
$\mathsf{\alpha }$	coefficient of linear heat expansion of the coating material
$\mathsf{\kappa }$	the thermal diffusivity of the coating material
$f$	the coefficient of friction
$K^{*}$	the proportionality coefficient between the work of friction forces and the volume of removed material
$K$	the thermal conductivity of the coating material
$k$	the heat transfer coefficient through the coating–substrate interface
$u_w(t)$	coating wear
$Q(t)$	the amount of frictional heat originated at the contact interface
$\Delta (t)$	the law of indentation of a hard abrasive (half-plane I) into the coating