Multidimensional transonic shock waves and free boundary problems

We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments and corresponding related nonlinear partial differential (PDEs) mixed type. The PDEs under our include steady potential flow, full equations, unsteady elliptic–hyperbolic problem flow past solid wedges, von Neumann reflection–diffraction, Prandtl–Meyer supersonic onto wedges. first show how these longstanding can be formulated as Then present an effective method ideas techniques to solve problems. method, ideas, should useful analyze other newly emerging PDEs.