Effect of the medium inhomogeneity on the evolution equation of plane shock waves

Using the method of matched asymptotic expansions, solutions of boundary-value problems of shock deformation of nonlinear elastic weakly inhomogeneous semispaces are obtained. It is shown that nonlinearity of the model and various properties of the inhomogeneity lead to new evolution equations in the frontal areas of longitudinal and transverse shock waves, the transition to which is due to transformations of all independent coordinates of the problem.