Abstract:
In 1956 Frankl, while studying subsonic flows past a profile with a supersonic
zone terminating with a normal compression shock, arrived at a new mathematical
problem for the Chaplygin equation with a non-local boundary condition. In this
article we give a survey of classical and recent papers dedicated to this problem.
We present theorems on the existence and uniqueness of the solution of the Frankl
problem, study the spectral problem for the Lavrent'ev–Bitsadze operator,
show applications of these results to the construction of a solution with the aid
of a series, and state some unsolved problems.
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