Global entropy solutions to exothermically reacting, compressible Euler equations (Q1399892)

The system of equations \(v_t -u_y =0\), \(u_t +p_y =0\), \(E_t + (pu)_y = qY\Phi (T),\) \(Y_t =-Y\Phi (T)\), describes compressible flows which undergo a one-step exothermal chemical reaction. The pressure \(p\) and the temperature \(T\) are given through the internal energy function \(e(v,S,\varepsilon)\) by the formulas \(p=-e_v (v,S,\varepsilon),\) \(T=\) \(e_S (v,S,\varepsilon),\) where \(v=1/\rho\) is the specific volume, \(S\) is the entropy. The reaction rate function \(\Phi (T)\) is given by the Arrhenius form. When the small parameter \(\varepsilon\) vanishes, the function \(e(v,S,\varepsilon)\) corresponds to the ideal gas. The global existence of entropy solution to the Cauchy problem is proved under certain restrictions on the total variation of initial data.