Shock-generated ignition: the induction zone

Solutions of the small disturbance equations for shock-induced thermal explosions at high activation energies are discussed in the limit when the adiabatic and isothermal sound speeds lie close together. Temperature and pressure perturbations are shown to possess logarithmic singularities at ignition. Although the density perturbation appears to have a similar behaviour, a local adjustment occurs exponentially close to the ignition point and the density at ignition is bounded. Excellent agreement with numerical calculations is found.