-
Previous Article
Optimal power for an elliptic equation related to some Caffarelli-Kohn-Nirenberg inequalities
- CPAA Home
- This Issue
-
Next Article
Global dynamics above the ground state for the energy-critical Schrödinger equation with radial data
Uniform global existence and convergence of Euler-Maxwell systems with small parameters
1. | 20 Rue de Vialle, Lamothe, 43100, France |
References:
[1] |
G. Alì, Global existence of smooth solutions of the $N$-Dimensional Euler-Poisson model,, \emph{SIAM J. Appl. Math.}, 35 (2003), 389.
doi: 10.1137/S0036141001393225. |
[2] |
G. Alì, L. Chen, A. Jungel and Y.-J. Peng, The zero-electron-mass limit in the hydrodynamic models for plasmas,, \emph{Nonlinear Analysis TMA}, 72 (2010), 4410.
doi: 10.1016/j.na.2010.02.016. |
[3] |
C. Besse, P. Degond, F. Deluzet, J. Claudel, G. Gallice and C. Tessieras, A model hierarchy for ionospheric plasma modeling,, \emph{Math. Models Methods Appl. Sci.}, 14 (2004), 393.
doi: 10.1142/S0218202504003283. |
[4] |
S. Bianchini, B. Hanouzet and R. Natalini, Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy,, \emph{Comm. Pure Appl. Math.}, 60 (2007), 1559.
doi: 10.1002/cpa.20195. |
[5] |
Y. Brenier, N. Mauser and M. Puel, Incompressible Euler and e-MHD as scaling limits of the Vlasov-Maxwell system,, \emph{Comm. Math. Sci.}, 1 (2003), 437.
|
[6] |
G. Carbou, B. Hanouzet and R. Natalini, Semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation,, \emph{J. Differential Equations}, 246 (2009), 291.
doi: 10.1016/j.jde.2008.05.015. |
[7] |
J. Y. Chemin, Fluides Parfaits Incompressibles,, Ast\'erisque No. 230, (1995).
|
[8] |
F. Chen, Introduction to Plasma Physics and Controlled Fusion,, Vol. 1, (1984). |
[9] |
G. Q. Chen, J. W. Jerome and D. Wang, Compressible Euler-Maxwell equations,, \emph{Transport theory and statistical physics}, 29 (2000), 311.
doi: 10.1080/00411450008205877. |
[10] |
J. F. Coulombel and T. Goudon, The strong relaxation limit of the multidimensional isothermal Euler equations,, \emph{Transactions Amer. Math. Soc.}, 359 (2007), 637.
doi: 10.1090/S0002-9947-06-04028-1. |
[11] |
P. Degond, F. Deluzet and D. Savelief, Numerical approximation of the Euler-Maxwell model in the quasineutral limit,, \emph{Journal of computational physics}, 231 (2012), 1917.
doi: 10.1016/j.jcp.2011.11.011. |
[12] |
R. J. Duan, Global smooth flows for the compressible Euler-Maxwell system : the relaxation case,, \emph{J. Hyper. Diff. Equations}, 8 (2011), 375.
doi: 10.1142/S0219891611002421. |
[13] |
W. Fang and K. Ito, Global solutions of the time-dependent drift-diffusion semiconductor equations,, \emph{J. Differential Equations}, 123 (1995), 523.
doi: 10.1006/jdeq.1995.1172. |
[14] |
P. Germain and N. Masmoudi, Global existence for the Euler-Maxwell system,, \emph{Annales Scientifiques de l'ENS}, 47 (2014), 469.
|
[15] |
Y. Guo, A. D. Ionescu and B. Pausader, Global solutions of the Euler-Maxwell two-fluid system in 3D,, preprint, ().
doi: 10.4007/annals.2016.183.2.1. |
[16] |
B. Hanouzet and R. Natalini, Global existence of smooth solutions for partial dissipative hyperbolic systems with a convex entropy,, \emph{Arch. Ration. Mech. Anal.}, 169 (2003), 89.
doi: 10.1007/s00205-003-0257-6. |
[17] |
L. Hsiao, P. A. Markowich and S. Wang, The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors,, \emph{J. Differential Equations}, 192 (2003), 111.
doi: 10.1016/S0022-0396(03)00063-9. |
[18] |
A. D. Ionescu and B. Pausader, Global solutions of quasilinear systems of Klein-Gordon equations in 3D,, \emph{J. Eur. Math. Soc.}, 16 (2014), 2355.
doi: 10.4171/JEMS/489. |
[19] |
A. Jüngel, On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors,, \emph{Math. Models Methods Appl. Sci.}, 4 (1994), 677.
doi: 10.1142/S0218202594000388. |
[20] |
A. Jüngel and Y. J. Peng, A hierarchy of hydrodynamic models for plasmas: Zero-relaxation-time limits,, \emph{Comm. Partial Differential Equations}, 24 (1999), 1007.
doi: 10.1080/03605309908821456. |
[21] |
T. Kato, The Cauchy problem for quasilinear symmetric hyperbolic systems,, \emph{Arch. Ration. Mech. Anal.}, 58 (1975), 181.
|
[22] |
S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids,, \emph{Comm. Pure Math. Appl.}, 34 (1981), 481.
doi: 10.1002/cpa.3160340405. |
[23] |
C. Lattanzio, On the 3-D bipolar isentropic Euler-Poisson model for semi-conductors and the drift-diffusion limit,, \emph{Math. Models Methods Appl. Sci.}, 10 (2000), 351.
doi: 10.1142/S0218202500000215. |
[24] |
C. Lattanzio and P. Marcati, The relaxation to the drift-diffusion system for the 3-D isentropic Euler-Poisson model for semiconductors,, \emph{Discrete Contin. Dyn. Syst.}, 5 (1999), 449.
doi: 10.3934/dcds.1999.5.449. |
[25] |
C. Lin and J. F. Coulombel, The strong relaxation limit of the multidimensional Euler equations,, \emph{NoDEA Nonlinear Differential Equations Appl.}, 20 (2013), 447.
doi: 10.1007/s00030-012-0159-0. |
[26] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables,, Springer-Verlag, (1984).
doi: 10.1007/978-1-4612-1116-7. |
[27] |
P. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equations,, \emph{Arch. Ration. Mech. Anal.}, 129 (1995), 129.
doi: 10.1007/BF00379918. |
[28] |
P. A. Markowich, C. A. Ringhofer and C. Shmeiser, Semiconductor Equations,, Springer-Verlag, (1990).
doi: 10.1007/978-3-7091-6961-2. |
[29] |
Y. J. Peng and S. Wang, Convergence of compressible Euler-Maxwell equations to compressible Euler-Poisson equations,, \emph{Chinese Annals of Mathematics}, 28-B (2007), 583.
doi: 10.1007/s11401-005-0556-3. |
[30] |
Y. J. Peng and S. Wang, Convergence of compressible Euler-Maxwell equations to incompressible Euler equations,, \emph{Communications in Partial Differential Equations}, 33 (2008), 349.
doi: 10.1080/03605300701318989. |
[31] |
Y. J. Peng and S. Wang, Rigorous derivation of incompressible e-MHD equations from compressible Euler-Maxwell equations,, \emph{SIAM J. Math. Anal.}, 40 (2008), 349.
doi: 10.1137/070686056. |
[32] |
Y. J. Peng, S. Wang and Q. Gu, Relaxation limit and global existence of smooth solutions of compressible Euler-Maxwell equations,, \emph{SIAM J. Math. Anal.}, 43 (2011), 944.
doi: 10.1137/100786927. |
[33] |
Y. J. Peng, Stability of non-constant equilibrium solutions for Euler-Maxwell equations,, \emph{J. Math. Pure Appl.}, 103 (2015), 39.
doi: 10.1016/j.matpur.2014.03.007. |
[34] |
Y. J. Peng, Uniformly global smooth solutions and convergence of Euler-Poisson systems with small parameters,, \emph{SIAM J. Math. Anal.}, 47 (2015), 1355.
doi: 10.1137/140983276. |
[35] |
Y. J. Peng and V. Wasiolek, Parabolic limits with differential constraints of first-order quasilinear hyperbolic systems,, \emph{Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire}, AN (2015). |
[36] |
Y. J. Peng and V. Wasiolek, Uniform global existence and parabolic limit for partially dissipative hyperbolic Systems,, preprint., ().
doi: 10.1016/j.jde.2016.01.019. |
[37] |
Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation,, \emph{Hokkaido Math. J.}, 14 (1985), 249.
doi: 10.14492/hokmj/1381757663. |
[38] |
J. Simon, Compact sets in the space $L^p(0, T; B)$,, \emph{Ann. Mat. Pura Appl.}, 146 (1987), 65.
doi: 10.1007/BF01762360. |
[39] |
B. Texier, WKB asymptotics for the Euler-Maxwell equations,, \emph{Asymptot. Anal.}, 42 (2005), 211.
|
[40] |
B. Texier, Derivation of the Zakharov equations,, \emph{Arch. Ration. Mech. Anal.}, 184 (2007), 121.
doi: 10.1007/s00205-006-0034-4. |
[41] |
Y. Ueda and S. Kawashima, Decay property of regularity-loss type for the Euler-Maxwell system,, \emph{Methods Appl. Anal.}, 18 (2011), 245.
doi: 10.4310/MAA.2011.v18.n3.a1. |
[42] |
W. A. Yong, Diffusive relaxation limit of multidimensional isentropic hydrodynamical models for semiconductors,, \emph{SIAM J. Appl. Math.}, 64 (2004), 1737.
doi: 10.1137/S0036139903427404. |
[43] |
W. A. Yong, Entropy and global existence for hyperbolic balance laws,, \emph{Arch. Ration. Mech. Anal.}, 172 (2004), 247.
doi: 10.1007/s00205-003-0304-3. |
[44] |
Y. Zeng, Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation,, \emph{Arch. Ration. Mech. Anal.}, 150 (1999), 225.
doi: 10.1007/s002050050188. |
show all references
References:
[1] |
G. Alì, Global existence of smooth solutions of the $N$-Dimensional Euler-Poisson model,, \emph{SIAM J. Appl. Math.}, 35 (2003), 389.
doi: 10.1137/S0036141001393225. |
[2] |
G. Alì, L. Chen, A. Jungel and Y.-J. Peng, The zero-electron-mass limit in the hydrodynamic models for plasmas,, \emph{Nonlinear Analysis TMA}, 72 (2010), 4410.
doi: 10.1016/j.na.2010.02.016. |
[3] |
C. Besse, P. Degond, F. Deluzet, J. Claudel, G. Gallice and C. Tessieras, A model hierarchy for ionospheric plasma modeling,, \emph{Math. Models Methods Appl. Sci.}, 14 (2004), 393.
doi: 10.1142/S0218202504003283. |
[4] |
S. Bianchini, B. Hanouzet and R. Natalini, Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy,, \emph{Comm. Pure Appl. Math.}, 60 (2007), 1559.
doi: 10.1002/cpa.20195. |
[5] |
Y. Brenier, N. Mauser and M. Puel, Incompressible Euler and e-MHD as scaling limits of the Vlasov-Maxwell system,, \emph{Comm. Math. Sci.}, 1 (2003), 437.
|
[6] |
G. Carbou, B. Hanouzet and R. Natalini, Semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation,, \emph{J. Differential Equations}, 246 (2009), 291.
doi: 10.1016/j.jde.2008.05.015. |
[7] |
J. Y. Chemin, Fluides Parfaits Incompressibles,, Ast\'erisque No. 230, (1995).
|
[8] |
F. Chen, Introduction to Plasma Physics and Controlled Fusion,, Vol. 1, (1984). |
[9] |
G. Q. Chen, J. W. Jerome and D. Wang, Compressible Euler-Maxwell equations,, \emph{Transport theory and statistical physics}, 29 (2000), 311.
doi: 10.1080/00411450008205877. |
[10] |
J. F. Coulombel and T. Goudon, The strong relaxation limit of the multidimensional isothermal Euler equations,, \emph{Transactions Amer. Math. Soc.}, 359 (2007), 637.
doi: 10.1090/S0002-9947-06-04028-1. |
[11] |
P. Degond, F. Deluzet and D. Savelief, Numerical approximation of the Euler-Maxwell model in the quasineutral limit,, \emph{Journal of computational physics}, 231 (2012), 1917.
doi: 10.1016/j.jcp.2011.11.011. |
[12] |
R. J. Duan, Global smooth flows for the compressible Euler-Maxwell system : the relaxation case,, \emph{J. Hyper. Diff. Equations}, 8 (2011), 375.
doi: 10.1142/S0219891611002421. |
[13] |
W. Fang and K. Ito, Global solutions of the time-dependent drift-diffusion semiconductor equations,, \emph{J. Differential Equations}, 123 (1995), 523.
doi: 10.1006/jdeq.1995.1172. |
[14] |
P. Germain and N. Masmoudi, Global existence for the Euler-Maxwell system,, \emph{Annales Scientifiques de l'ENS}, 47 (2014), 469.
|
[15] |
Y. Guo, A. D. Ionescu and B. Pausader, Global solutions of the Euler-Maxwell two-fluid system in 3D,, preprint, ().
doi: 10.4007/annals.2016.183.2.1. |
[16] |
B. Hanouzet and R. Natalini, Global existence of smooth solutions for partial dissipative hyperbolic systems with a convex entropy,, \emph{Arch. Ration. Mech. Anal.}, 169 (2003), 89.
doi: 10.1007/s00205-003-0257-6. |
[17] |
L. Hsiao, P. A. Markowich and S. Wang, The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors,, \emph{J. Differential Equations}, 192 (2003), 111.
doi: 10.1016/S0022-0396(03)00063-9. |
[18] |
A. D. Ionescu and B. Pausader, Global solutions of quasilinear systems of Klein-Gordon equations in 3D,, \emph{J. Eur. Math. Soc.}, 16 (2014), 2355.
doi: 10.4171/JEMS/489. |
[19] |
A. Jüngel, On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors,, \emph{Math. Models Methods Appl. Sci.}, 4 (1994), 677.
doi: 10.1142/S0218202594000388. |
[20] |
A. Jüngel and Y. J. Peng, A hierarchy of hydrodynamic models for plasmas: Zero-relaxation-time limits,, \emph{Comm. Partial Differential Equations}, 24 (1999), 1007.
doi: 10.1080/03605309908821456. |
[21] |
T. Kato, The Cauchy problem for quasilinear symmetric hyperbolic systems,, \emph{Arch. Ration. Mech. Anal.}, 58 (1975), 181.
|
[22] |
S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids,, \emph{Comm. Pure Math. Appl.}, 34 (1981), 481.
doi: 10.1002/cpa.3160340405. |
[23] |
C. Lattanzio, On the 3-D bipolar isentropic Euler-Poisson model for semi-conductors and the drift-diffusion limit,, \emph{Math. Models Methods Appl. Sci.}, 10 (2000), 351.
doi: 10.1142/S0218202500000215. |
[24] |
C. Lattanzio and P. Marcati, The relaxation to the drift-diffusion system for the 3-D isentropic Euler-Poisson model for semiconductors,, \emph{Discrete Contin. Dyn. Syst.}, 5 (1999), 449.
doi: 10.3934/dcds.1999.5.449. |
[25] |
C. Lin and J. F. Coulombel, The strong relaxation limit of the multidimensional Euler equations,, \emph{NoDEA Nonlinear Differential Equations Appl.}, 20 (2013), 447.
doi: 10.1007/s00030-012-0159-0. |
[26] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables,, Springer-Verlag, (1984).
doi: 10.1007/978-1-4612-1116-7. |
[27] |
P. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equations,, \emph{Arch. Ration. Mech. Anal.}, 129 (1995), 129.
doi: 10.1007/BF00379918. |
[28] |
P. A. Markowich, C. A. Ringhofer and C. Shmeiser, Semiconductor Equations,, Springer-Verlag, (1990).
doi: 10.1007/978-3-7091-6961-2. |
[29] |
Y. J. Peng and S. Wang, Convergence of compressible Euler-Maxwell equations to compressible Euler-Poisson equations,, \emph{Chinese Annals of Mathematics}, 28-B (2007), 583.
doi: 10.1007/s11401-005-0556-3. |
[30] |
Y. J. Peng and S. Wang, Convergence of compressible Euler-Maxwell equations to incompressible Euler equations,, \emph{Communications in Partial Differential Equations}, 33 (2008), 349.
doi: 10.1080/03605300701318989. |
[31] |
Y. J. Peng and S. Wang, Rigorous derivation of incompressible e-MHD equations from compressible Euler-Maxwell equations,, \emph{SIAM J. Math. Anal.}, 40 (2008), 349.
doi: 10.1137/070686056. |
[32] |
Y. J. Peng, S. Wang and Q. Gu, Relaxation limit and global existence of smooth solutions of compressible Euler-Maxwell equations,, \emph{SIAM J. Math. Anal.}, 43 (2011), 944.
doi: 10.1137/100786927. |
[33] |
Y. J. Peng, Stability of non-constant equilibrium solutions for Euler-Maxwell equations,, \emph{J. Math. Pure Appl.}, 103 (2015), 39.
doi: 10.1016/j.matpur.2014.03.007. |
[34] |
Y. J. Peng, Uniformly global smooth solutions and convergence of Euler-Poisson systems with small parameters,, \emph{SIAM J. Math. Anal.}, 47 (2015), 1355.
doi: 10.1137/140983276. |
[35] |
Y. J. Peng and V. Wasiolek, Parabolic limits with differential constraints of first-order quasilinear hyperbolic systems,, \emph{Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire}, AN (2015). |
[36] |
Y. J. Peng and V. Wasiolek, Uniform global existence and parabolic limit for partially dissipative hyperbolic Systems,, preprint., ().
doi: 10.1016/j.jde.2016.01.019. |
[37] |
Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation,, \emph{Hokkaido Math. J.}, 14 (1985), 249.
doi: 10.14492/hokmj/1381757663. |
[38] |
J. Simon, Compact sets in the space $L^p(0, T; B)$,, \emph{Ann. Mat. Pura Appl.}, 146 (1987), 65.
doi: 10.1007/BF01762360. |
[39] |
B. Texier, WKB asymptotics for the Euler-Maxwell equations,, \emph{Asymptot. Anal.}, 42 (2005), 211.
|
[40] |
B. Texier, Derivation of the Zakharov equations,, \emph{Arch. Ration. Mech. Anal.}, 184 (2007), 121.
doi: 10.1007/s00205-006-0034-4. |
[41] |
Y. Ueda and S. Kawashima, Decay property of regularity-loss type for the Euler-Maxwell system,, \emph{Methods Appl. Anal.}, 18 (2011), 245.
doi: 10.4310/MAA.2011.v18.n3.a1. |
[42] |
W. A. Yong, Diffusive relaxation limit of multidimensional isentropic hydrodynamical models for semiconductors,, \emph{SIAM J. Appl. Math.}, 64 (2004), 1737.
doi: 10.1137/S0036139903427404. |
[43] |
W. A. Yong, Entropy and global existence for hyperbolic balance laws,, \emph{Arch. Ration. Mech. Anal.}, 172 (2004), 247.
doi: 10.1007/s00205-003-0304-3. |
[44] |
Y. Zeng, Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation,, \emph{Arch. Ration. Mech. Anal.}, 150 (1999), 225.
doi: 10.1007/s002050050188. |
[1] |
Jiang Xu, Wen-An Yong. Zero-relaxation limit of non-isentropic hydrodynamic models for semiconductors. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1319-1332. doi: 10.3934/dcds.2009.25.1319 |
[2] |
Jianwei Yang, Ruxu Lian, Shu Wang. Incompressible type euler as scaling limit of compressible Euler-Maxwell equations. Communications on Pure & Applied Analysis, 2013, 12 (1) : 503-518. doi: 10.3934/cpaa.2013.12.503 |
[3] |
Yachun Li, Xucai Ren. Non-relativistic global limits of the entropy solutions to the relativistic Euler equations with $\gamma$-law. Communications on Pure & Applied Analysis, 2006, 5 (4) : 963-979. doi: 10.3934/cpaa.2006.5.963 |
[4] |
Xingwen Hao, Yachun Li, Zejun Wang. Non-relativistic global limits to the three dimensional relativistic euler equations with spherical symmetry. Communications on Pure & Applied Analysis, 2010, 9 (2) : 365-386. doi: 10.3934/cpaa.2010.9.365 |
[5] |
Jiang Xu, Ting Zhang. Zero-electron-mass limit of Euler-Poisson equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4743-4768. doi: 10.3934/dcds.2013.33.4743 |
[6] |
Sebastian Bauer. A non-relativistic model of plasma physics containing a radiation reaction term. Kinetic & Related Models, 2018, 11 (1) : 25-42. doi: 10.3934/krm.2018002 |
[7] |
Yachun Li, Qiufang Shi. Global existence of the entropy solutions to the isentropic relativistic Euler equations. Communications on Pure & Applied Analysis, 2005, 4 (4) : 763-778. doi: 10.3934/cpaa.2005.4.763 |
[8] |
Marina Ghisi, Massimo Gobbino. Hyperbolic--parabolic singular perturbation for mildly degenerate Kirchhoff equations: Global-in-time error estimates. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1313-1332. doi: 10.3934/cpaa.2009.8.1313 |
[9] |
Jackson Itikawa, Jaume Llibre, Ana Cristina Mereu, Regilene Oliveira. Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3259-3272. doi: 10.3934/dcdsb.2017136 |
[10] |
Jihua Yang, Liqin Zhao. Limit cycle bifurcations for piecewise smooth integrable differential systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2417-2425. doi: 10.3934/dcdsb.2017123 |
[11] |
Dingheng Pi. Limit cycles for regularized piecewise smooth systems with a switching manifold of codimension two. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 881-905. doi: 10.3934/dcdsb.2018211 |
[12] |
Hirotada Honda. Global-in-time solution and stability of Kuramoto-Sakaguchi equation under non-local Coupling. Networks & Heterogeneous Media, 2017, 12 (1) : 25-57. doi: 10.3934/nhm.2017002 |
[13] |
Yue-Jun Peng, Shu Wang. Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 415-433. doi: 10.3934/dcds.2009.23.415 |
[14] |
Stephen Pankavich, Nicholas Michalowski. Global classical solutions for the "One and one-half'' dimensional relativistic Vlasov-Maxwell-Fokker-Planck system. Kinetic & Related Models, 2015, 8 (1) : 169-199. doi: 10.3934/krm.2015.8.169 |
[15] |
Piotr Biler, Ignacio Guerra, Grzegorz Karch. Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2117-2126. doi: 10.3934/cpaa.2015.14.2117 |
[16] |
Weizhu Bao, Chunmei Su. Uniform error estimates of a finite difference method for the Klein-Gordon-Schrödinger system in the nonrelativistic and massless limit regimes. Kinetic & Related Models, 2018, 11 (4) : 1037-1062. doi: 10.3934/krm.2018040 |
[17] |
Li Fang, Zhenhua Guo. Zero dissipation limit to rarefaction wave with vacuum for a one-dimensional compressible non-Newtonian fluid. Communications on Pure & Applied Analysis, 2017, 16 (1) : 209-242. doi: 10.3934/cpaa.2017010 |
[18] |
Huijiang Zhao, Yinchuan Zhao. Convergence to strong nonlinear rarefaction waves for global smooth solutions of $p-$system with relaxation. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1243-1262. doi: 10.3934/dcds.2003.9.1243 |
[19] |
Michael Zgurovsky, Mark Gluzman, Nataliia Gorban, Pavlo Kasyanov, Liliia Paliichuk, Olha Khomenko. Uniform global attractors for non-autonomous dissipative dynamical systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 2053-2065. doi: 10.3934/dcdsb.2017120 |
[20] |
Georgia Karali, Takashi Suzuki, Yoshio Yamada. Global-in-time behavior of the solution to a Gierer-Meinhardt system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 2885-2900. doi: 10.3934/dcds.2013.33.2885 |
2017 Impact Factor: 0.884
Tools
Metrics
Other articles
by authors
[Back to Top]