Semi-hyperbolic patches of solutions of the pressure gradient system (Q833285)

The authors study special self-similar solutions to the 2-D pressure gradient system \(u_t+p_x=v_t+p_y=E_t+(up)_x+(vp)_y=0\), where \(E=p+(u^2+v^2)/2\). They construct patches of solutions, in which one family of characteristics starts on sonic curves and ends on transonic shock waves. This type of solutions seems to be common for two-dimensional Riemann problems. Since these solutions are situated middle-way between the fully hyperbolic and elliptic regions the authors call them semi-hyperbolic. The semi-hyperbolic patches of solutions are intended to use as building tiles in construction of global solutions for general Riemann problems.