A global subsonic solution to an interacting transonic shock for the self-similar nonlinear wave equation |
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Authors: | Eun Heui Kim |
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Institution: | Department of Mathematics, California State University, Long Beach, CA 90840-1001, United States |
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Abstract: | We present 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. 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, we show the well-posedness of the transonic shock in the entire subsonic region and thus establish the global solution. This result does not rely on any smallness of Riemann data. |
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Keywords: | primary 35L65 35L70 35R35 secondary 35M10 35J65 76J20 |
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