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Classification of bifurcation diagrams of a $P$-Laplacian nonpositone problem
The expansion of gas from a wedge with small angle into a vacuum
1. | School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
References:
[1] |
X. Chen and Y. X. Zheng, The interaction of rarefaction waves of the two-dimensional Euler equations, Indiana Univ. Math. J, 59 (2010), 231-256.
doi: 10.1512/iumj.2010.59.3752. |
[2] |
R. Courant and K. O. Friedrichs, "Supersonic Flow and Shock Waves,'' Reprinting of the 1948 original. Applied Mathematical Sciences, 21. Springer-Verlag, New York-Heidelberg, 1976. |
[3] |
X. M. Ji and Y. X. Zheng, Characteristic decouplings and interactions of rarefaction waves of 2-D Euler equations, J. Math. Anal. Appl., (2012).
doi: 10.1016/j.jmaa.2012.05.035. |
[4] |
L. E. Levine, The expansion of a wedge of gas into a vacuum, Proc. Camb. Phil. Soc., 64 (1968), 1151-1163.
doi: 10.1017/S0305004100043899. |
[5] |
J. Q. Li, On the two-dimensional gas expansion for compressible Euler equations, SIAM J. Math. Anal., 62 (2001), 831-852.
doi: 10.1137/S0036139900361349. |
[6] |
J. Q. Li, Global solution of an initial value problem for two-dimensional compressible Euler equations, J. Differ. Eqs., 179 (2002), 178-194.
doi: 10.1006/jdeq.2001.4025. |
[7] |
J. Q. Li, Z. C. Yang and Y. X. Zheng, Characteristic decompositions and interactions of rarefaction waves of 2-D Euler equations, J. Differ. Eqs., 250 (2011), 782-798.
doi: 10.1016/j.jde.2010.07.009. |
[8] |
J. Q. Li, T. Zhang and S. L. Yang, "The Two-dimensional Riemann Problem in Gas Dynamics," $\pi$ Pitman Monographs and Surveys in Pure and Applied Mathematics, 98. Longman, Harlow, 1998. |
[9] |
J. Q. Li and Y. X. Zheng, Interaction of rarefaction waves of the two-dimensional self-similar Euler equations, Arch. Ration. Mech. Anal., 193 (2009), 623-657.
doi: 10.1007/s00205-008-0140-6. |
[10] |
M. J. Li and Y. X. Zheng, Semi-hyperbolic patches of solutions of the two-dimensional Euler equations, Arch. Ration. Mech. Anal., 201 (2011), 1069-1096.
doi: 10.1007/s00205-011-0410-6. |
[11] |
T. Li and T. H. Qin, Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms, Chinese Annals of Mathematics, 6 (1985), 199-210. |
[12] |
T. Li and W. C. Yu, "Boundary Value Problems for Quasilinear Hyperbolic Systems,'' Duke University Mathematics Series V, 1985. |
[13] |
P. Qu, $C^0$ sstimate for a kind of partially dissipative quasilinear hyperbolic systems and its applications, in manuscript. |
[14] |
V. A. Suchkov, Flow into a vacuum along an oblique wall, J. Appl. Math. Mech., 27 (1963), 1132-1134.
doi: 10.1016/0021-8928(63)90195-3. |
[15] |
Y. X. Zheng, "Systems of Conservation Laws: Two-dimensional Riemann Problems,'' Progress in Nonlinear Differential Equations and Their Applications, 38, Birkhäuser, Boston, 2001. |
show all references
References:
[1] |
X. Chen and Y. X. Zheng, The interaction of rarefaction waves of the two-dimensional Euler equations, Indiana Univ. Math. J, 59 (2010), 231-256.
doi: 10.1512/iumj.2010.59.3752. |
[2] |
R. Courant and K. O. Friedrichs, "Supersonic Flow and Shock Waves,'' Reprinting of the 1948 original. Applied Mathematical Sciences, 21. Springer-Verlag, New York-Heidelberg, 1976. |
[3] |
X. M. Ji and Y. X. Zheng, Characteristic decouplings and interactions of rarefaction waves of 2-D Euler equations, J. Math. Anal. Appl., (2012).
doi: 10.1016/j.jmaa.2012.05.035. |
[4] |
L. E. Levine, The expansion of a wedge of gas into a vacuum, Proc. Camb. Phil. Soc., 64 (1968), 1151-1163.
doi: 10.1017/S0305004100043899. |
[5] |
J. Q. Li, On the two-dimensional gas expansion for compressible Euler equations, SIAM J. Math. Anal., 62 (2001), 831-852.
doi: 10.1137/S0036139900361349. |
[6] |
J. Q. Li, Global solution of an initial value problem for two-dimensional compressible Euler equations, J. Differ. Eqs., 179 (2002), 178-194.
doi: 10.1006/jdeq.2001.4025. |
[7] |
J. Q. Li, Z. C. Yang and Y. X. Zheng, Characteristic decompositions and interactions of rarefaction waves of 2-D Euler equations, J. Differ. Eqs., 250 (2011), 782-798.
doi: 10.1016/j.jde.2010.07.009. |
[8] |
J. Q. Li, T. Zhang and S. L. Yang, "The Two-dimensional Riemann Problem in Gas Dynamics," $\pi$ Pitman Monographs and Surveys in Pure and Applied Mathematics, 98. Longman, Harlow, 1998. |
[9] |
J. Q. Li and Y. X. Zheng, Interaction of rarefaction waves of the two-dimensional self-similar Euler equations, Arch. Ration. Mech. Anal., 193 (2009), 623-657.
doi: 10.1007/s00205-008-0140-6. |
[10] |
M. J. Li and Y. X. Zheng, Semi-hyperbolic patches of solutions of the two-dimensional Euler equations, Arch. Ration. Mech. Anal., 201 (2011), 1069-1096.
doi: 10.1007/s00205-011-0410-6. |
[11] |
T. Li and T. H. Qin, Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms, Chinese Annals of Mathematics, 6 (1985), 199-210. |
[12] |
T. Li and W. C. Yu, "Boundary Value Problems for Quasilinear Hyperbolic Systems,'' Duke University Mathematics Series V, 1985. |
[13] |
P. Qu, $C^0$ sstimate for a kind of partially dissipative quasilinear hyperbolic systems and its applications, in manuscript. |
[14] |
V. A. Suchkov, Flow into a vacuum along an oblique wall, J. Appl. Math. Mech., 27 (1963), 1132-1134.
doi: 10.1016/0021-8928(63)90195-3. |
[15] |
Y. X. Zheng, "Systems of Conservation Laws: Two-dimensional Riemann Problems,'' Progress in Nonlinear Differential Equations and Their Applications, 38, Birkhäuser, Boston, 2001. |
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