On the structure of wave fronts in nonlinear dissipative media

Abstract

Wave fronts are well known to be the regions of space where the properties of motion vary sharply in a certain direction. This means that one of the components of the gradients of density, velocity, stress, etc., at the wave fronts exceeds essentially not only other components but also corresponding gradients outside the fronts. The large gradients require that the analysis of motion within the fronts (the front structure) be based on equations more detailed than those sufficient in the surroundings. Meanwhile these more detailed equations admit simplification of the boundary-layer type because the fronts are necessarily slender in one direction. In the “external” approximation the fronts are represented by discontinuity surfaces (Figure 1, a).