Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 243, pp. 120.
Properties of solutions in semihyperbolic patches for
unsteady transonic small disturbance equations
Ilija Jegdic, Katarina Jegdic
Abstract:
We consider a twodimensional Riemann problem for the unsteady transonic small
disturbance equation resulting in diverging rarefaction waves.
We write the problem in selfsimilar coordinates and we obtain a mixed
type (hyperbolicelliptic) system.
Resolving the onedimensional discontinuities in the far field, where
the system is hyperbolic, and using characteristics, we formulate the
problem in a semihyperbolic patch that is between the hyperbolic and
the elliptic regions. A semihyperbolic 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 semihyperbolic 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; semihyperbolic patch; Goursattype 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


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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