The problem of flow about infinite plane wedge with inviscous non-heat-conducting gas. Linear stability of a weak shock wave

摘要

We study the classical problem for a flow of stationary inviscid non-heat-conducting gas in thermody-namical equilibrium moving onto a planar infinite wedge. Under the fulfillment of the weak Lopatinski condition on the shock (neutral stability), the well-posedness of the linearized initial boundary value problem (when the main solution is a weak shock) is proven and a representation of the classical solution is obtained. Unlike the case when the uniform Lopatinski condition holds, i.e. the attached shock is uniformly (strongly) stable, in this representation, additional plane waves appear. For compactly supported initial data, the solution reaches a prescribed regime in finite time.