The unsteady transonic small disturbance equation: Data on oblique curves
Mary Chern, Barbara Lee Keyfitz · Discrete and Continuous Dynamical Systems · 2016
We propose and solve a new problem for the unsteady transonicsmall disturbance equation.Data are given for the self-similar equation in a fixed, bounded region ofsimilarity space, where on a part of the boundary the equation has degeneratetype (a `sonic line') and on the remainder it is elliptic.Previous results on this problem have chosen data so that the solution is constanton the sonic line, but we set up a situation where thesolution 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 problemsfor this equation and for other multidimensional conservation laws.