-
Previous Article
Sampling, feasibility, and priors in data assimilation
- DCDS Home
- This Issue
-
Next Article
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), 194-207.
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), 548-574.
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), 319-340.
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), 71-92. |
[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), 1365-1393.
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), 1067-1182.
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), 63-100.
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), 1347-1448.
doi: 10.1002/cpa.20231. |
[9] |
G. Fichera, Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine, Atti della Accademia Nazionale dei Lincei, Cl. Sci. Fis. Mat. Nat. Ser. I, 5 (1956), 1-30. |
[10] |
G. Fichera, On a unified theory of boundary value problems for elliptic- parabolic equations of second order, In R. E. Langer, editor, Boundary Problems in Differential Equations, pages 97-120. University of Wisconsin, Madison, 1960. |
[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), 124-143.
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, ().
|
[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, editors, Free and Moving Boundaries: Analysis, Simulation and Control, pages 125-163. CRC Press, Boca Raton, 2007.
doi: 10.1201/9781420011159.ch6. |
[14] |
B. L. Keyfitz, Self-similar solutions of two-dimensional conservation laws, Journal of Hyperbolic Differential Equations, 1 (2004), 445-492.
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), 83-94. |
[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), 119-133.
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, Providence, 1973. |
[18] |
M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations, Springer-Verlag, New York, 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), 1874-1892.
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), 42-61.
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), 317-338.
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), 1360-1377.
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), 194-207.
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), 548-574.
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), 319-340.
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), 71-92. |
[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), 1365-1393.
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), 1067-1182.
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), 63-100.
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), 1347-1448.
doi: 10.1002/cpa.20231. |
[9] |
G. Fichera, Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine, Atti della Accademia Nazionale dei Lincei, Cl. Sci. Fis. Mat. Nat. Ser. I, 5 (1956), 1-30. |
[10] |
G. Fichera, On a unified theory of boundary value problems for elliptic- parabolic equations of second order, In R. E. Langer, editor, Boundary Problems in Differential Equations, pages 97-120. University of Wisconsin, Madison, 1960. |
[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), 124-143.
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, ().
|
[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, editors, Free and Moving Boundaries: Analysis, Simulation and Control, pages 125-163. CRC Press, Boca Raton, 2007.
doi: 10.1201/9781420011159.ch6. |
[14] |
B. L. Keyfitz, Self-similar solutions of two-dimensional conservation laws, Journal of Hyperbolic Differential Equations, 1 (2004), 445-492.
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), 83-94. |
[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), 119-133.
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, Providence, 1973. |
[18] |
M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations, Springer-Verlag, New York, 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), 1874-1892.
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), 42-61.
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), 317-338.
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), 1360-1377.
doi: 10.1137/070698567. |
[1] |
K. T. Joseph, Philippe G. LeFloch. Boundary layers in weak solutions of hyperbolic conservation laws II. self-similar vanishing diffusion limits. Communications on Pure and Applied Analysis, 2002, 1 (1) : 51-76. doi: 10.3934/cpaa.2002.1.51 |
[2] |
Weronika Biedrzycka, Marta Tyran-Kamińska. Self-similar solutions of fragmentation equations revisited. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 13-27. doi: 10.3934/dcdsb.2018002 |
[3] |
Mapundi K. Banda, Michael Herty. Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws. Mathematical Control and Related Fields, 2013, 3 (2) : 121-142. doi: 10.3934/mcrf.2013.3.121 |
[4] |
Yu Zhang, Yanyan Zhang. Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1523-1545. doi: 10.3934/cpaa.2019073 |
[5] |
Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 143-145. doi: 10.3934/dcds.2000.6.143 |
[6] |
Anna Chiara Lai, Paola Loreti. Self-similar control systems and applications to zygodactyl bird's foot. Networks and Heterogeneous Media, 2015, 10 (2) : 401-419. doi: 10.3934/nhm.2015.10.401 |
[7] |
Qiaolin He. Numerical simulation and self-similar analysis of singular solutions of Prandtl equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (1) : 101-116. doi: 10.3934/dcdsb.2010.13.101 |
[8] |
F. Berezovskaya, G. Karev. Bifurcations of self-similar solutions of the Fokker-Plank equations. Conference Publications, 2005, 2005 (Special) : 91-99. doi: 10.3934/proc.2005.2005.91 |
[9] |
Alberto Bressan, Wen Shen. A posteriori error estimates for self-similar solutions to the Euler equations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 113-130. doi: 10.3934/dcds.2020168 |
[10] |
Hyungjin Huh. Self-similar solutions to nonlinear Dirac equations and an application to nonuniqueness. Evolution Equations and Control Theory, 2018, 7 (1) : 53-60. doi: 10.3934/eect.2018003 |
[11] |
Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 673-682. doi: 10.3934/dcds.2000.6.673 |
[12] |
Gui-Qiang Chen, Monica Torres. On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1011-1036. doi: 10.3934/cpaa.2011.10.1011 |
[13] |
Stefano Bianchini. A note on singular limits to hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2003, 2 (1) : 51-64. doi: 10.3934/cpaa.2003.2.51 |
[14] |
Fumioki Asakura, Andrea Corli. The path decomposition technique for systems of hyperbolic conservation laws. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 15-32. doi: 10.3934/dcdss.2016.9.15 |
[15] |
Marco Cannone, Grzegorz Karch. On self-similar solutions to the homogeneous Boltzmann equation. Kinetic and Related Models, 2013, 6 (4) : 801-808. doi: 10.3934/krm.2013.6.801 |
[16] |
Thomas Y. Hou, Ruo Li. Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 637-642. doi: 10.3934/dcds.2007.18.637 |
[17] |
Dongho Chae, Kyungkeun Kang, Jihoon Lee. Notes on the asymptotically self-similar singularities in the Euler and the Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1181-1193. doi: 10.3934/dcds.2009.25.1181 |
[18] |
Jochen Merker, Aleš Matas. Positivity of self-similar solutions of doubly nonlinear reaction-diffusion equations. Conference Publications, 2015, 2015 (special) : 817-825. doi: 10.3934/proc.2015.0817 |
[19] |
Hideo Kubo, Kotaro Tsugawa. Global solutions and self-similar solutions of the coupled system of semilinear wave equations in three space dimensions. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 471-482. doi: 10.3934/dcds.2003.9.471 |
[20] |
Zoran Grujić. Regularity of forward-in-time self-similar solutions to the 3D Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2006, 14 (4) : 837-843. doi: 10.3934/dcds.2006.14.837 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]