< Compressible Flow Papers (last updated September 2005) >


Two-dimensional Riemann problems
Transonic regular reflection for the nonlinear wave system. [with K. Jegdic and B. L. Keyfitz]
Journal of Hyperbolic Differential Equations, , 3(3) (2006), 443-375.
A Riemann Problem for the isentropic gas dynamics equations. [with K. Jegdic and B. L. Keyfitz]
Proceedings of the MSRI/AWM Workshop ``The Legacy of Ladizhenskaya and Oleinik.'', Berkeley, CA, , (2006) 165-170.
Free Boundary Problems for Nonlinear Wave Systems: Interacting Shocks. [with B. L. Keyfitz and Kim E.H] (pdf)
SIAM J. Mathematical Analysis , Vol. 37(6) (2006) 1947 -1977 .
Transonic regular reflection for the nonlinear wave system. [with K. Jegdic and B. L. Keyfitz] ()
Journal of Hyperbolic Differential Equations 3(3) (2006),443 -375. ,
Transonic regular reflection for the Unsteady Transonic Small Disturbance Equation - details of the subsonic solution. [with K. Jegdic and B. L. Keyfitz] ()
Proceedings of the IFIP Conference 2005. Accepted. , (2005).
Mixed Hyperbolic-Elliptic Systems in Self-Similar Flows [with B. L. Keyfitz and Kim E.H] ()
Bulletin of the Brasilian Mathematical Society , Vol. 32(3) (2001).
Self-similar Problems in Multi-dimensional Conservation Laws [with B. L. Keyfitz and Kim E.H] ()
Proceedings of IC-SEC Conference on Recent Advance in Computational Science and Engineering, Singapore , December 2002. ,
Riemann problems for the two-dimensional unsteady transonic small disturbance equation [with Keyfitz] (ps)
SIAM Journal on Applied Mathematics, Vol. 58(2) (1998).
A numerical study of Riemann problems for the two-dimensional unsteady transonic small disturbance equation [with Mirkovic] (ps)
SIAM Journal on Applied Mathematics, Vol. 58(5),1365 - 1393(1998).
Quasi-one-dimensional Riemann problems and their role in self-similar two-dimensional problems [with Keyfitz]
Archive for Rational Mechanics and Analysis, 144 (1998),223 -258.
A useful class of two-dimensional conservation laws [with Keyfitz]
Mathematical Research, Vol 87, eds. K. Kirchgaessner et al., Akademie Verlag Berlin (1996), pp. 133-137.

Weak shock reflection
A free boundary problem for a quasilinear degenerate elliptic equation: regular reflection of weak shocks [with Keyfitz and Kim] (ps)
Communications on Pure and Applied Mathematics, Vol. LV (2002)71 -92.
Free boundary problems for the unsteady transonic small disturbance equation: transonic regular reflection [with Keyfitz and Kim] (ps)
Methods and Applications of Analysis, 7 (2) (2000)313 -336.
A proof of existence of perturbed steady transonic shocks via a free-boundary problem [with Keyfitz and Lieberman] (ps)
Communications in Pure and Applied Mathematics, Vol. LIII (2000), 484-511.
Weak shock reflection modeled by the unsteady transonic small disturbance equation [with Keyfitz and Lieberman] (ps)
Hyperbolic Problems: Theory, Numerics, Applications, Vol. 141 (1) (2000)217 -226.
Oblique shock interactions and the von Newmann Paradox [with Keyfitz] (ps)
Proc. 20th International Conference on Shock Waves, Vol. I (eds. Sturtevant B., Schepherd J.E., Hornung H.G.).
A bifurcation diagram for oblique shock interactions in the unsteady transonic small disturbance equation [with Keyfitz and Wagner]
Hyperbolic Problems: Theory, Numerics, and Applications, Editors: Glimm et al., World Scientific, Singapore (1996), pp. 178-187.

Nonlinear degenerate elliptic equations
An elliptic problem arising from the unsteady transonic small disturbance equation [with Keyfitz] (ps)
Journal of Differential Equations, Vol. 125 (1996), pp. 548-574.
A smooth solution for a Keldysh type equation [with Keyfitz] (ps)
Communications in Partial Differential Equations, Vol. 21 (1996), pp. 319-340.
A class of quasilinear degenerate elliptic problems [with Eun Heui Kim] (ps)
Journal of Differential Equations, 189(1) (2003) 71-98.

Shock wave admissibility for conservation laws that change type
Shock wave admissibility for quadratic conservation laws [with Plohr] (ps)
Journal of Differential Equations, Vol. 118 (1995), pp. 293-335.
The role of limit cycles in the admissibility of shock waves
Matematica Contemporanea, Vol. 8 (1995), pp. 63-88.
Quadratic systems of conservation laws with generic behavior at infinity (ps)
Journal of Dynamics and Differential Equations, Vol. 9(3) (1997), pp. 401-426.
A global approach to shock wave admissibility
Anais do 19th Coloquio Brasileiro Matematica, (1992), pp. 199-216.
On the influence of viscosity on Riemann solutions (ps)
Journal of Dynamics and Differential Equations, Vol. 9(4) (1997), pp. 663-703.
Nonexistence of Riemann solutions for a quadratic model deriving from petroleum engineering
Nonlinear Analysis: Real World Applications, Vol. 3(4) (2002) 629-665.
Oscillation waves in systems of conservation laws [with G. Peters] (ps)
Nonlinear Analysis: Series B.
Nonexistence of Riemann solutions and Majda-Pego instability [with G. Peters] (ps)
Journal of Differential Equations 172(1) (2001) 1-28.

Shock capturing for slowly moving shocks
Computations of slowly moving shocks [with S. Karni]
Journal of Computational Physics (136) 1997, no. 1, pp. 132-139.