The Riemann Problem in Gas Dynamics

We consider the Riemann problem (R.P.) for the <!-- MATH $3\, \times \, 3$ --> system of gas dynamics equations in a single space variable. We assume that the specific internal energy <!-- MATH $e = e(v,\,s)$ --> (s = specific entropy, v = specific volume) satisfies the usual hypotheses, <!-- MATH ${p_v}\, < \,0,\,{p_{vv}}\, > \,0,\,{p_s}\, > \,0\,(p\, = \, - \,{e_v}\, =$ --> <img width="342" height="41" align="MIDDLE" border="0" src="images/img3.gif" alt="$ {p_v}\, < \,0,\,{p_{vv}}\, > \,0,\,{p_s}\, > \,0\,(p\, = \, - \,{e_v}\, = $"> pressure); we also assume some reasonable hypotheses about the asymptotic behavior of e. We call functions e satisfying these hypotheses energy functions