Blast Waves in Multi-Component Medium with Thermal Relaxation

The mathematical models of relaxing media with a structure for describing nonlinear long-wave processes are explored. The wave processes in non-equilibrium heterogeneous media are studied in terms of the suggested asymptotic averaged model. On the microstructure level of the medium, the dynamical behavior is governed only by the laws of thermodynamics, while, on the macrolevel, the motion of the medium can be described by the wave-dynamical laws. It is proved rigorously that on the acoustic level, the propagation of long waves can be properly described only in terms of dispersive dissipative properties of the medium, and in this case, the dynamical behavior of the medium can be modeled by a homogeneous relaxing medium. At the same time, the dynamical behavior of the medium cannot be modeled by a homogeneous medium even for long waves, if they are nonlinear. For a finite-amplitude wave, the structure of medium produces nonlinear ef-fects even if the individual components of the medium are described by a linear law. The hetero-geneity of the structure of medium always introduces additional nonlinearity. It is shown that the solution of many problems for multi-component media with incompressible phases can be ob-tained through the known solution of a similar problem for a homogeneous compressible mediu