American Institute of Mathematical Sciences

August  2016, 36(8): 4213-4225. doi: 10.3934/dcds.2016.36.4213

The unsteady transonic small disturbance equation: Data on oblique curves

 1 Fields Institute, United States 2 Department of Mathematics, The Ohio State University, Columbus, OH 43210, United States

Received  May 2015 Revised  November 2015 Published  March 2016

We propose and solve a new problem for the unsteady transonic small disturbance equation. Data are given for the self-similar equation in a fixed, bounded region of similarity space, where on a part of the boundary the equation has degenerate type (a `sonic line') and on the remainder it is elliptic. Previous results on this problem have chosen data so that the solution is constant on the sonic line, but we set up a situation where the solution is not constant on the sonic part of the boundary. The solution we find is Lipschitz up to the boundary. Our solution sets the stage for resolution of some interesting Riemann problems for this equation and for other multidimensional conservation laws.
Citation: Mary Chern, Barbara Lee Keyfitz. The unsteady transonic small disturbance equation: Data on oblique curves. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4213-4225. doi: 10.3934/dcds.2016.36.4213
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