Stability of a supersonic flow past a wedge with adjoint weak neutrally stable shock wave

We study the classical problem of a supersonic stationary flow of a nonviscous nonheat-conducting gas in local thermodynamic equilibrium past an infinite plane wedge. Under the Lopatinskiĭ­ condition on the shock wave (neutral stability), we prove the well-posedness of the linearized mixed problem (the main solution is a weak shock wave), obtain a representation of the classical solution, where, in this case (in contrast to the case of the uniform Lopatinskiĭ­ condition — an absolutely stable shock wave), plane waves additionally appear in the representation. If the initial data have compact support, the solution reaches the given regime in infinite time.