The three-dimensional problem on the mutual wear of a thin elastic layer and a punch sliding on it

A three-dimensional problem on the contact interaction between a thin elastic layer and an absolutely rigid body sliding over it is considered where wear of both bodies is assumed. The solution is represented by a Fourier series, the coefficients of which are found in an explicit form. The asymptotics of the contact pressure for large times are investigated. The importance of taking the factor of the mutual wear of the contacting bodies into account is demonstrated.