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Super polyharmonic property of solutions for PDE systems and its applications
Local uniqueness of steady spherical transonic shock-fronts for the three--dimensional full Euler equations
1. | School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
2. | Department of Mathematics, East China Normal University, Shanghai 200241, China |
References:
[1] |
P. Amorim, M. Ben-Artzi and P. G. LeFloch, Hyperbolic conservation laws on manifolds: Total variation estimates and the finite volume method,, Methods Appl. Anal., 12 (2005), 291.
|
[2] |
P. Amorim, P. G. LeFloch and W. Neves, A geometric approach to error estimates for conservation laws posed on a spacetime,, Nonlinear Anal., 74 (2011), 4898.
|
[3] |
D. Bleecker and G. Csordas, "Basic Partial Differential Equations,", International Press: Boston, (1996).
|
[4] |
G.-Q. Chen, C. M. Dafermos, M. Slemrod and D. Wang, On two-dimensional sonic-subsonic flow,, Comm. Math. Phys., 271 (2007), 635.
|
[5] |
G.-Q. Chen and M. Feldman, Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type,, J. Amer. Math. Soc., 16 (2003), 461.
|
[6] |
G.-Q. Chen and M. Feldman, Steady transonic shocks and free boundary problems in infinite cylinders for the Euler equations,, Comm. Pure Appl. Math., 57 (2004), 310.
|
[7] |
G.-Q. Chen and M. Feldman, Existence and stability of multidimensional transonic flows through an infinite nozzle of arbitrary cross-sections,, Arch. Rational Mech. Anal., 184 (2007), 185.
|
[8] |
G.-Q. Chen, J. Chen and M. Feldman, Transonic shocks and free boundary problems for the full Euler equations in infinite nozzles,, J. Math. Pures Appl., 88 (2007), 191.
|
[9] |
S. Chen and H. Yuan, Transonic shocks in compressible flow passing a duct for three-dimensional Euler systems,, Arch. Rational Mech. Anal., 187 (2008), 523.
|
[10] |
R. Courant and K. O. Friedrichs, "Supersonic Flow and Shock Waves,", Interscience Publishers Inc., (1948).
|
[11] |
C. M. Dafermos, "Hyperbolic Conservation Laws in Continuum Physics,", Springer-Verlag, (2000).
|
[12] |
T. Frankel, "The Geometry of Physicist, An Introduction,", 2nd Ed., (2004).
|
[13] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order,", 2nd Edition, (1983).
|
[14] |
T.-T. Li, "Global Classical Solutions for Quasilinear Hyperbolic Systems,", John Wiley & Sons, (1994).
|
[15] |
L. Liu and H. Yuan, Stability of cylindrical transonic shocks for two-dimensional steady compressible Euler system,, J. Hyper. Diff. Equ., 5 (2008), 347.
|
[16] |
Y. Luo and N. S. Trudinger, Linear second order elliptic equations with venttsel boundary conditions,, Proc. Royal Soc. Edinburgh, 118A (1991), 193.
|
[17] |
L. M. Sibner and R. J. Sibner, Transonic flows on axially symmetric torus,, J. Math. Anal. Appl., 72 (1979), 362.
|
[18] |
M. Taylor, "Partial Differential Equations,", Vol. 3, (1996).
|
[19] |
B. Whitham, "Linear and Nonlinear Waves,", John Wiley, (1974).
|
[20] |
H. Yuan, Examples of steady subsonic flows in a convergent-divergent approximate nozzle,, J. Diff. Eqs., 244 (2008), 1675.
|
[21] |
H. Yuan, On transonic shocks in two-dimensional variable-area ducts for steady Euler system,, SIAM J. Math. Anal., 38 (2006), 1343.
|
[22] |
H. Yuan, A remark on determination of transonic shocks in divergent nozzles for steady compressible Euler flows,, Nonlinear Analysis: Real World Appl., 9 (2008), 316.
|
show all references
References:
[1] |
P. Amorim, M. Ben-Artzi and P. G. LeFloch, Hyperbolic conservation laws on manifolds: Total variation estimates and the finite volume method,, Methods Appl. Anal., 12 (2005), 291.
|
[2] |
P. Amorim, P. G. LeFloch and W. Neves, A geometric approach to error estimates for conservation laws posed on a spacetime,, Nonlinear Anal., 74 (2011), 4898.
|
[3] |
D. Bleecker and G. Csordas, "Basic Partial Differential Equations,", International Press: Boston, (1996).
|
[4] |
G.-Q. Chen, C. M. Dafermos, M. Slemrod and D. Wang, On two-dimensional sonic-subsonic flow,, Comm. Math. Phys., 271 (2007), 635.
|
[5] |
G.-Q. Chen and M. Feldman, Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type,, J. Amer. Math. Soc., 16 (2003), 461.
|
[6] |
G.-Q. Chen and M. Feldman, Steady transonic shocks and free boundary problems in infinite cylinders for the Euler equations,, Comm. Pure Appl. Math., 57 (2004), 310.
|
[7] |
G.-Q. Chen and M. Feldman, Existence and stability of multidimensional transonic flows through an infinite nozzle of arbitrary cross-sections,, Arch. Rational Mech. Anal., 184 (2007), 185.
|
[8] |
G.-Q. Chen, J. Chen and M. Feldman, Transonic shocks and free boundary problems for the full Euler equations in infinite nozzles,, J. Math. Pures Appl., 88 (2007), 191.
|
[9] |
S. Chen and H. Yuan, Transonic shocks in compressible flow passing a duct for three-dimensional Euler systems,, Arch. Rational Mech. Anal., 187 (2008), 523.
|
[10] |
R. Courant and K. O. Friedrichs, "Supersonic Flow and Shock Waves,", Interscience Publishers Inc., (1948).
|
[11] |
C. M. Dafermos, "Hyperbolic Conservation Laws in Continuum Physics,", Springer-Verlag, (2000).
|
[12] |
T. Frankel, "The Geometry of Physicist, An Introduction,", 2nd Ed., (2004).
|
[13] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order,", 2nd Edition, (1983).
|
[14] |
T.-T. Li, "Global Classical Solutions for Quasilinear Hyperbolic Systems,", John Wiley & Sons, (1994).
|
[15] |
L. Liu and H. Yuan, Stability of cylindrical transonic shocks for two-dimensional steady compressible Euler system,, J. Hyper. Diff. Equ., 5 (2008), 347.
|
[16] |
Y. Luo and N. S. Trudinger, Linear second order elliptic equations with venttsel boundary conditions,, Proc. Royal Soc. Edinburgh, 118A (1991), 193.
|
[17] |
L. M. Sibner and R. J. Sibner, Transonic flows on axially symmetric torus,, J. Math. Anal. Appl., 72 (1979), 362.
|
[18] |
M. Taylor, "Partial Differential Equations,", Vol. 3, (1996).
|
[19] |
B. Whitham, "Linear and Nonlinear Waves,", John Wiley, (1974).
|
[20] |
H. Yuan, Examples of steady subsonic flows in a convergent-divergent approximate nozzle,, J. Diff. Eqs., 244 (2008), 1675.
|
[21] |
H. Yuan, On transonic shocks in two-dimensional variable-area ducts for steady Euler system,, SIAM J. Math. Anal., 38 (2006), 1343.
|
[22] |
H. Yuan, A remark on determination of transonic shocks in divergent nozzles for steady compressible Euler flows,, Nonlinear Analysis: Real World Appl., 9 (2008), 316.
|
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