A global subsonic solution to an interacting transonic shock for the self-similar nonlinear wave equation
The existence of the subsonic solution to a two-dimensional Riemann problem governed by a self-similar nonlinear wave equation where the boundary of the subsonic region consists of a transonic shock and the sonic circle is presented. Thus the governing equation becomes a free boundary problem on the transonic shock and degenerates on the sonic circle. By utilizing the barrier methods and iterative methods, the well-posedness of the transonic shock in the entire subsonic region is shown and thus the global solution is established. This result does not rely on any smallness of Riemann data.
scientific article; zbMATH DE number 5726574
scientific article