Abstract
The paper is concerned with the theoretical description of focusing weak, N-shaped shock waves. The shock rise times of the incoming shock fronts are assumed to be very small, but finite. Furthermore, focusing is assumed to be caused by only slightly concave wave fronts. The functional correspondence of refraction effects included already in a linear wave theory and steepening effects described by nonlinear wave theories are discussed in details by singular perturbation methods. Preliminary numerical evaluations of the resulting implicit solution agree well with known experimental data.
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