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Excerpt from A Well Posed Boundary Value Problem in Transonic Gas Dynamics
The problem of calculating continuous transonic flow past such an airfoil was shown by C. Morawetz [20] to be not well posed.
Motivated by the method of complex characteristics, a transonic boundary value problem was developed in [9] for a certain domain obtained by analytic extension to complex values of the independent variables. Complex conjugate characteristic coordinates E and n were introduced. In these coordinates the stream function is real in the subsonic domain but complex otherwise. The new boundary value problem is set by prescribing the real part of on the boundary of the unit circle. This problem has, as yet, not been shown to be well posed, although its numerical solution was found successfully. Our contribution will be to show that a corresponding problem for the Tricomi equation is well posed.
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Excerpt from A Well Posed Boundary Value Problem in Transonic Gas Dynamics
The problem of calculating continuous transonic flow past such an airfoil was shown by C. Morawetz [20] to be not well posed.
Motivated by the method of complex characteristics, a transonic boundary value problem was developed in [9] for a certain domain obtained by analytic extension to complex values of the independent variables. Complex conjugate characteristic coordinates E and n were introduced. In these coordinates the stream function is real in the subsonic domain but complex otherwise. The new boundary value problem is set by prescribing the real part of on the boundary of the unit circle. This problem has, as yet, not been shown to be well posed, although its numerical solution was found successfully. Our contribution will be to show that a corresponding problem for the Tricomi equation is well posed.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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