Some comments on wave motions described by non-homogeneous quasilinear first order hyperbolic systems

Abstract

In this paper a quasilinear first order hyperbolic system of partial differential equations involving a source term is considered. Thus in the usual context of the n-dimensional nonlinear wave propagation theory it is shown that the source term may produce attenuation effects against the typical nonlinear steepening of the waves. Therefore, by generalizing Whitham's ideas[9], [10], it is possible to introduce a «reduced system» of field equations which gives an approximate description of the wave process. Then, in an asymptotic way, it is possible to point out that in a wave motion governed by the reduced system there is a coupling between nonlinearity and dissipative (or dispersive) effects. A typical physical example where the present theory may be applied is shown at the end of the paper.