Weak solutions with a shock to a model system of the radiating gas. (English) Zbl 0915.76074

The paper deals with a reduced model for polytropic gas with radiative heat flow. This model consists of a Burgers type equation coupled with an elliptic linear equation: \(u_t + u u_x + q_x = 0\), \(-q_{xx} + q + u_x = 0\), for which the Riemann problem is investigated. It is shown that for \(u_->u_+\), there exists a unique weak solution according to a specified entropy criterion. Moreover, if \(| u_--u_+| \leq\frac{1}{2}\), then the solution is global and converges to a travelling wave with decay rate \(t^{-1/4}\). Travelling waves are studied in a companion paper that has appeared in SIAM J. Math. Anal. 30, No. 1, 95-117 (1999).
Reviewer: S.Benzoni (Lyon)


76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)