Communications in Mathematical Sciences

Volume 13 (2015)

Number 7

Global weak solutions to 1D compressible Euler equations with radiation

Pages: 1905 – 1936

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n7.a11

Authors

Xavier Blanc (Laboratoire Jacques-Louis Lions,Université de Paris Diderot, Paris, France)

Bernard Ducomet (CEA, Arpajon, France)

Abstract

We consider the Cauchy problem for the equations of one-dimensional motion of a compressible inviscid gas coupled with radiation through a radiative transfer equation. Assuming suitable hypotheses on the transport coefficients and the data, we prove that the problem admits a weak solution. More precisely, we show that a sequence of approximate solutions constructed by a generalized Glimm scheme admits a subsequence converging to an entropic solution of the problem.

Keywords

compressible, one-dimensional symmetry, radiative transfer

2010 Mathematics Subject Classification

35Q30, 76N10

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Published 19 August 2015