Abstract: The inverse problem for the supersonic plane flow described by TSD equation past a curved wedge is considered. For a uniform supersonic oncoming flow, under the hypothesis that the position of the shock is given, we will globally determine the curved wedge. This kind of problem plays an important role in the aviation industry. Under suitable assumptions, with the help of Riemann invariants and Lax transform, by solving a generalized Cauchy problem, the global existence and uniqueness for the above mentioned problem is established.

Key words: TSD equation, Riemann invariants, Lax transform, Generalized Cauchy problem