WAVE PROPAGATION PHENOMENA GOVERNED BY A MODIFIED KORTEWEG-DE VRIES-BURGERS EQUATION WITH MIXED NONLINEARITY

摘要

Previous investigations of nonlinear wave propagation phenomena have led to the interesting result that under certain conditions the evolution of waves is governed by a modified Korteweg-de Vries-Burgers (mKdVB) equation where the flux function exhibits an additional cubic term. The analysis presented here focuses on the properties of this equation in the limit of vanishing dissipative as well as dispersive effects. As it will turn out, then the identification of physically acceptable weak solutions has to be approached by a special regularization principle based on the fact that the resulting hyperbolic evolution equation with mixed nonlinearity is still embedded in a structure involving dissipation and dispersion. Consequently, the thus obtained shock admissibility criteria for the insertion of discontinuities crucially depend on the precise ratio of dispersion to dissipation in the system, even though these effects are assumed to be small. This may lead to unsteady solutions violating the well-known Lax entropy criterion since their jumps emanate rather than absorb waves.