Stability of planar shock fronts for multidimensional systems of relaxation equations (Q639490)

This paper is concerned with the stability and the large time behavior of multi-dimensional planar shocks of hyperbolic relaxation systems. Indeed, it generalizes the results of scalar relaxation case to the system, and it discusses stability with the asymptotic behavior along with decay rates of small amplitude multidimensional planar shocks under certain assumption. Attention is focused on the standard case of a classical Lax-type shock. The semigroup approach and energy method are exploited to establish low frequency and high frequency bonds, respectively. The system equilibrium case is treated in a manner similar to the one for inviscid and viscous systems under the constant multiplicity condition.