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Symbolic extensions and partially hyperbolic diffeomorphisms
Asymptotic analysis of a diffuse interface relaxation to a nonlocal optimal partition problem
1. | Department of Mathematics, Pennsylvania State University, University Park, PA 16802 |
2. | Department of Mathematics, Pennsylvania Sate University, University Park, PA 16802, United States |
References:
[1] |
W. Bao, Ground states and dynamics of multi-component Bose-Einstein condensates, SIAM Multiscale Model. Simulat., 2 (2004), 210-236.
doi: 10.1137/030600209. |
[2] |
W. Bao and Q. Du, Comuputing the ground state solution of Bose-Einstein condensates by a normalized gradient flow, SIAM J. Sci. Comput., 25 (2004), 1674-1697.
doi: 10.1137/S1064827503422956. |
[3] |
H. Berestycki, T. C. Lin, J. Wei and C. Zhao, On phase-separation model: Asymptotics and qualitative properties, preprint, 2010. |
[4] |
V. Bonnaillie-Noel, B. Helffer and G. Vial, Numerical simulations for nodal domains and spectral minimal partitions, ESAIM: COCV, 16 (2010), 221-246.
doi: 10.1051/cocv:2008074. |
[5] |
L. A. Cafferelli and F. H. Lin, An optimal partition problem for eigenvalues, Journal of Scientific Computing, 31 (2007), 5-18.
doi: 10.1007/s10915-006-9114-8. |
[6] |
L. A. Cafferelli and F. H. Lin, Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries, J. Amer. Math. Soc., 21 (2008), 847-862.
doi: 10.1090/S0894-0347-08-00593-6. |
[7] |
L. A. Cafferrelli and F. H. Lin, Nonlocal heat flows preserving the $L^2$ energy, Discrete and Continuous Dynamical Systems A, 23 (2009), 49-64. |
[8] |
S.-M. Chang, C.-S. Lin, T.-C. Lin and W.-W. Lin, Segregated nodal domains of two dimensional multispecies Bose-Einstein condensates, Phys. D, 196 (2004), 341-361.
doi: 10.1016/j.physd.2004.06.002. |
[9] |
S.-M. Chang, W.-W. Lin and S.-F. Shieh, Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate, J. of Computational Physics, 202 (2005), 367-390
doi: 10.1016/j.jcp.2004.07.012. |
[10] |
M. Conti, S. Terracini and G. Verzini, Nehari's problem and competing species systems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 19 (2002), 871-888.
doi: 10.1016/S0294-1449(02)00104-X. |
[11] |
M. Conti, S. Terracini and G. Verzini, A variational problem for the spatial segregation of reaction-diffusion systems, Indiana Univ. Math. J., 54 (2005), 779-815.
doi: 10.1512/iumj.2005.54.2506. |
[12] |
M. Conti, S. Terracini and G. Verzini, Asymptotic estimates for the spatial segregation of competitive systems, Adv. Math., 195 (2005), 524-560.
doi: 10.1016/j.aim.2004.08.006. |
[13] |
Q. Du and F.-H. Lin, Numerical approximations of a norm preserving nonlinear gradient flow and applications to an optimal partition problem, Nonlinearity, 22 (2009), 67-83.
doi: 10.1088/0951-7715/22/1/005. |
[14] |
T.-C. Lin and J. Wei, Ground state of n coupled nonlinear schrodinger equations in $R^n$, $n\leq 3$, Comm. Math. Phys., 255 (2005), 629-653.
doi: 10.1007/s00220-005-1313-x. |
[15] |
J. Wei and T. Weth, Asymptotic behaviour of solutions of planar elliptic systems with strong competition, Nonlinearity, 21 (2008), 305-317.
doi: 10.1088/0951-7715/21/2/006. |
show all references
References:
[1] |
W. Bao, Ground states and dynamics of multi-component Bose-Einstein condensates, SIAM Multiscale Model. Simulat., 2 (2004), 210-236.
doi: 10.1137/030600209. |
[2] |
W. Bao and Q. Du, Comuputing the ground state solution of Bose-Einstein condensates by a normalized gradient flow, SIAM J. Sci. Comput., 25 (2004), 1674-1697.
doi: 10.1137/S1064827503422956. |
[3] |
H. Berestycki, T. C. Lin, J. Wei and C. Zhao, On phase-separation model: Asymptotics and qualitative properties, preprint, 2010. |
[4] |
V. Bonnaillie-Noel, B. Helffer and G. Vial, Numerical simulations for nodal domains and spectral minimal partitions, ESAIM: COCV, 16 (2010), 221-246.
doi: 10.1051/cocv:2008074. |
[5] |
L. A. Cafferelli and F. H. Lin, An optimal partition problem for eigenvalues, Journal of Scientific Computing, 31 (2007), 5-18.
doi: 10.1007/s10915-006-9114-8. |
[6] |
L. A. Cafferelli and F. H. Lin, Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries, J. Amer. Math. Soc., 21 (2008), 847-862.
doi: 10.1090/S0894-0347-08-00593-6. |
[7] |
L. A. Cafferrelli and F. H. Lin, Nonlocal heat flows preserving the $L^2$ energy, Discrete and Continuous Dynamical Systems A, 23 (2009), 49-64. |
[8] |
S.-M. Chang, C.-S. Lin, T.-C. Lin and W.-W. Lin, Segregated nodal domains of two dimensional multispecies Bose-Einstein condensates, Phys. D, 196 (2004), 341-361.
doi: 10.1016/j.physd.2004.06.002. |
[9] |
S.-M. Chang, W.-W. Lin and S.-F. Shieh, Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate, J. of Computational Physics, 202 (2005), 367-390
doi: 10.1016/j.jcp.2004.07.012. |
[10] |
M. Conti, S. Terracini and G. Verzini, Nehari's problem and competing species systems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 19 (2002), 871-888.
doi: 10.1016/S0294-1449(02)00104-X. |
[11] |
M. Conti, S. Terracini and G. Verzini, A variational problem for the spatial segregation of reaction-diffusion systems, Indiana Univ. Math. J., 54 (2005), 779-815.
doi: 10.1512/iumj.2005.54.2506. |
[12] |
M. Conti, S. Terracini and G. Verzini, Asymptotic estimates for the spatial segregation of competitive systems, Adv. Math., 195 (2005), 524-560.
doi: 10.1016/j.aim.2004.08.006. |
[13] |
Q. Du and F.-H. Lin, Numerical approximations of a norm preserving nonlinear gradient flow and applications to an optimal partition problem, Nonlinearity, 22 (2009), 67-83.
doi: 10.1088/0951-7715/22/1/005. |
[14] |
T.-C. Lin and J. Wei, Ground state of n coupled nonlinear schrodinger equations in $R^n$, $n\leq 3$, Comm. Math. Phys., 255 (2005), 629-653.
doi: 10.1007/s00220-005-1313-x. |
[15] |
J. Wei and T. Weth, Asymptotic behaviour of solutions of planar elliptic systems with strong competition, Nonlinearity, 21 (2008), 305-317.
doi: 10.1088/0951-7715/21/2/006. |
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