Mathematical Modeling Of Explosive Processes In Inhomogeneous Stars

Abstract

The work considers a non-self-similar problem about the central explosion of nonhomogeneous gas body (star) bordering vacuum which is in equilibrium in its own gravitational field. To solve the problem, the asymptotic method of thin impact layer has been used. The solution of the problem in the vicinity behind the shock wave (the destruction surface of the first kind) is sought in the form of a singular asymptotic decomposition by a small parameter. Analytically, the main (zero) approximation for the law of motion and the thermodynamic characteristics of the medium has been accurately found. The Cauchy problem for zero approximation of the law of motion of the shock has been solved exactly, in the form of elliptic integrals of the first and second general ones. The relevant asymptotics have been found.