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Transonic flows with shocks past curved wedges for the full Euler equations
The unsteady transonic small disturbance equation: Data on oblique curves
1. | Fields Institute, United States |
2. | Department of Mathematics, The Ohio State University, Columbus, OH 43210, United States |
References:
[1] |
M. Brio and J. K. Hunter, Mach reflection for the two dimensional Burgers equation,, Physica D, 60 (1992), 194.
doi: 10.1016/0167-2789(92)90236-G. |
[2] |
S. Čanić and B. L. Keyfitz, An elliptic problem arising from the unsteady transonic small disturbance equation,, Journal of Differential Equations, 125 (1996), 548.
doi: 10.1006/jdeq.1996.0040. |
[3] |
S. Čanić and B. L. Keyfitz, A smooth solution for a Keldysh type equation,, Communications in Partial Differential Equations, 21 (1996), 319.
doi: 10.1080/03605309608821186. |
[4] |
S. Čanić, B. L. Keyfitz and E. H. Kim, A free boundary problem for a quasilinear degenerate elliptic equation: Regular reflection of weak shocks,, Communications on Pure and Applied Mathematics, LV (2002), 71. Google Scholar |
[5] |
S. Čanić and D. Mirković, A numerical study of shock reflection modeled by the unsteady transonic small disturbance equation,, SIAM Journal on Applied Mathematics, 58 (1998), 1365.
doi: 10.1137/S003613999730884X. |
[6] |
G.-Q. Chen and M. Feldman, Global solutions of shock reflection by large-angle wedges for potential flow,, Annals of Mathematics, 171 (2010), 1067.
doi: 10.4007/annals.2010.171.1067. |
[7] |
S.-X. Chen, Mach configuration in pseudo-stationary compressible flow,, Journal of the American Mathematical Society, 21 (2008), 63.
doi: 10.1090/S0894-0347-07-00559-0. |
[8] |
V. Elling and T.-P. Liu, Supersonic flow onto a solid wedge},, Communications on Pure and Applied Mathematics, 61 (2008), 1347.
doi: 10.1002/cpa.20231. |
[9] |
G. Fichera, Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine,, Atti della Accademia Nazionale dei Lincei, 5 (1956), 1.
|
[10] |
G. Fichera, On a unified theory of boundary value problems for elliptic- parabolic equations of second order,, In R. E. Langer, (1960), 97.
|
[11] |
J. K. Hunter and A. M. Tesdall, On the self-similar diffraction of a weak shock into an expansion wavefront,, SIAM Journal on Applied Mathematics, 72 (2012), 124.
doi: 10.1137/110834135. |
[12] |
I. Jegdić and K. Jegdić, Properties of solutions in semi-hyperbolic patches for the unsteady transonic small disturbance equation,, Electronic Journal of Differential Equations, (). Google Scholar |
[13] |
K. Jegdić, B. L. Keyfitz and S. Čanić, Transonic regular reflection for the unsteady transonic small disturbance equation - details of the subsonic solution,, In R. Glowinski and J. P. Zolesio, (2007), 125.
doi: 10.1201/9781420011159.ch6. |
[14] |
B. L. Keyfitz, Self-similar solutions of two-dimensional conservation laws,, Journal of Hyperbolic Differential Equations, 1 (2004), 445.
doi: 10.1142/S0219891604000160. |
[15] |
B. L. Keyfitz, The Fichera function and nonlinear equations,, Accademia Nazionale delle Scienze detta dei XL. Rendiconti. Serie V. Memorie di Matematica e Applicazioni. Parte I, 30 (2006), 83.
|
[16] |
B. L. Keyfitz, A. Tesdall, K. R. Payne and N. I. Popivanov, The sonic line as a free boundary,, Quarterly of Applied Mathematics, 71 (2013), 119.
doi: 10.1090/S0033-569X-2012-01283-6. |
[17] |
O. A. Oleĭnik and E. V. Radkevič, Second Order Equations with Nonnegative Characteristic Form,, American Mathematical Society, (1973).
|
[18] |
M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations,, Springer-Verlag, (1993).
|
[19] |
E. G. Tabak and R. R. Rosales, Focusing of weak shock waves and the von Neumann paradox of oblique shock reflection,, Physics of Fluids A, 6 (1994), 1874.
doi: 10.1063/1.868246. |
[20] |
A. M. Tesdall and J. K. Hunter, Self-similar solutions for weak shock reflection,, SIAM Journal on Applied Mathematics, 63 (2002), 42.
doi: 10.1137/S0036139901383826. |
[21] |
A. M. Tesdall and B. L. Keyfitz, A continuous, two-way free boundary in the unsteady transonic small disturbance equations,, Journal of Hyperbolic Differential Equations, 7 (2010), 317.
doi: 10.1142/S0219891610002153. |
[22] |
A. M. Tesdall, R. Sanders and B. L. Keyfitz, Self-similar solutions for the triple point paradox in gasdynamics,, SIAM Journal on Applied Mathematics, 68 (2008), 1360.
doi: 10.1137/070698567. |
show all references
References:
[1] |
M. Brio and J. K. Hunter, Mach reflection for the two dimensional Burgers equation,, Physica D, 60 (1992), 194.
doi: 10.1016/0167-2789(92)90236-G. |
[2] |
S. Čanić and B. L. Keyfitz, An elliptic problem arising from the unsteady transonic small disturbance equation,, Journal of Differential Equations, 125 (1996), 548.
doi: 10.1006/jdeq.1996.0040. |
[3] |
S. Čanić and B. L. Keyfitz, A smooth solution for a Keldysh type equation,, Communications in Partial Differential Equations, 21 (1996), 319.
doi: 10.1080/03605309608821186. |
[4] |
S. Čanić, B. L. Keyfitz and E. H. Kim, A free boundary problem for a quasilinear degenerate elliptic equation: Regular reflection of weak shocks,, Communications on Pure and Applied Mathematics, LV (2002), 71. Google Scholar |
[5] |
S. Čanić and D. Mirković, A numerical study of shock reflection modeled by the unsteady transonic small disturbance equation,, SIAM Journal on Applied Mathematics, 58 (1998), 1365.
doi: 10.1137/S003613999730884X. |
[6] |
G.-Q. Chen and M. Feldman, Global solutions of shock reflection by large-angle wedges for potential flow,, Annals of Mathematics, 171 (2010), 1067.
doi: 10.4007/annals.2010.171.1067. |
[7] |
S.-X. Chen, Mach configuration in pseudo-stationary compressible flow,, Journal of the American Mathematical Society, 21 (2008), 63.
doi: 10.1090/S0894-0347-07-00559-0. |
[8] |
V. Elling and T.-P. Liu, Supersonic flow onto a solid wedge},, Communications on Pure and Applied Mathematics, 61 (2008), 1347.
doi: 10.1002/cpa.20231. |
[9] |
G. Fichera, Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine,, Atti della Accademia Nazionale dei Lincei, 5 (1956), 1.
|
[10] |
G. Fichera, On a unified theory of boundary value problems for elliptic- parabolic equations of second order,, In R. E. Langer, (1960), 97.
|
[11] |
J. K. Hunter and A. M. Tesdall, On the self-similar diffraction of a weak shock into an expansion wavefront,, SIAM Journal on Applied Mathematics, 72 (2012), 124.
doi: 10.1137/110834135. |
[12] |
I. Jegdić and K. Jegdić, Properties of solutions in semi-hyperbolic patches for the unsteady transonic small disturbance equation,, Electronic Journal of Differential Equations, (). Google Scholar |
[13] |
K. Jegdić, B. L. Keyfitz and S. Čanić, Transonic regular reflection for the unsteady transonic small disturbance equation - details of the subsonic solution,, In R. Glowinski and J. P. Zolesio, (2007), 125.
doi: 10.1201/9781420011159.ch6. |
[14] |
B. L. Keyfitz, Self-similar solutions of two-dimensional conservation laws,, Journal of Hyperbolic Differential Equations, 1 (2004), 445.
doi: 10.1142/S0219891604000160. |
[15] |
B. L. Keyfitz, The Fichera function and nonlinear equations,, Accademia Nazionale delle Scienze detta dei XL. Rendiconti. Serie V. Memorie di Matematica e Applicazioni. Parte I, 30 (2006), 83.
|
[16] |
B. L. Keyfitz, A. Tesdall, K. R. Payne and N. I. Popivanov, The sonic line as a free boundary,, Quarterly of Applied Mathematics, 71 (2013), 119.
doi: 10.1090/S0033-569X-2012-01283-6. |
[17] |
O. A. Oleĭnik and E. V. Radkevič, Second Order Equations with Nonnegative Characteristic Form,, American Mathematical Society, (1973).
|
[18] |
M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations,, Springer-Verlag, (1993).
|
[19] |
E. G. Tabak and R. R. Rosales, Focusing of weak shock waves and the von Neumann paradox of oblique shock reflection,, Physics of Fluids A, 6 (1994), 1874.
doi: 10.1063/1.868246. |
[20] |
A. M. Tesdall and J. K. Hunter, Self-similar solutions for weak shock reflection,, SIAM Journal on Applied Mathematics, 63 (2002), 42.
doi: 10.1137/S0036139901383826. |
[21] |
A. M. Tesdall and B. L. Keyfitz, A continuous, two-way free boundary in the unsteady transonic small disturbance equations,, Journal of Hyperbolic Differential Equations, 7 (2010), 317.
doi: 10.1142/S0219891610002153. |
[22] |
A. M. Tesdall, R. Sanders and B. L. Keyfitz, Self-similar solutions for the triple point paradox in gasdynamics,, SIAM Journal on Applied Mathematics, 68 (2008), 1360.
doi: 10.1137/070698567. |
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