Ilija Jegdic, Katarina Jegdic
Abstract:
We consider a two-dimensional Riemann problem for the unsteady transonic small
disturbance equation resulting in diverging rarefaction waves.
We write the problem in self-similar coordinates and we obtain a mixed
type (hyperbolic-elliptic) system.
Resolving the one-dimensional discontinuities in the far field, where
the system is hyperbolic, and using characteristics, we formulate the
problem in a semi-hyperbolic patch that is between the hyperbolic and
the elliptic regions. A semi-hyperbolic patch is known as a region where
one family out of two nonlinear families of characteristics starts on a
sonic curve and ends on a transonic shock. We obtain existence of a smooth
local solution in this semi-hyperbolic patch and we prove various properties
of global smooth solutions based on a characteristic decomposition using
directional derivatives.
Submitted April 27, 2015. Published September 22, 2015.
Math Subject Classifications: 35L65.
Key Words: Unsteady transonic small disturbance equation;
mixed type system; semi-hyperbolic patch; Goursat-type problem.
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Ilija Jegdic Department of Mathematics and Physics Houston Baptist University 7502 Fondren Rd, Houston, TX 77074, USA email: i_jegdic@yahoo.com |
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Katarina Jegdic Department of Mathematics and Statistics University of Houston - Downtown 1 Main St, Houston, TX 77002, USA email: jegdick@uhd.edu |
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