AN EXISTENCE THEOREM FOR A FREE-BOUNDARY PROBLEM OF HYPERSONIC FLOW THEORY

The author considers a free boundary problem arising in hypersonic flo w theory. The model describes an axisymmetric thin viscous shock layer in the vicinity of the stagnation point of a blunt body. The governin g equations on the symmetry line reduce to a two-point boundary value problem with four unknowns and a free boundary. The free boundary prob lem is reduced to a nonlinear eigenvalue problem through a change of v ariable. Existence of a solution is achieved by deriving a priori esti mates and by using the Leray-Schauder topological degree theory.