We study hyperbolic totally characteristic boundary problems with an

additional degeneracy appearing at the edge formed of boundary and initial hypersurface. The spacetime domain has coordinates , the

prototypical example is provided by the second-order scalar differential operator

, where . The solution to the Cauchy problem

is found in a class of adapted 2-microlocal spaces. (No boundary conditions are

required due to the totally characteristic boundary.) Such problems arise when steady supersonic flow turns a sufficiently large bend and a vacuum region separates from the flow.

This is joint work with Ruan Zhuoping (NJU, Nanjing).

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