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On a mathematical model arising from competition of Phytoplankton species for a single nutrient with internal storage: steady state analysis
A particle method and numerical study of a quasilinear partial differential equation
1. | The University of North Carolina at Chapel Hill, Phillips Hall, CB #3250, Chapel Hill, NC 27599-3250, United States |
2. | Nuclear Engineering Division, Institute of Nuclear Energy Research, Taoyuan County, 32546, Taiwan |
3. | Department of Mathematics, University of Wyoming, Laramie, WY 82071-3036, United States |
4. | Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei City 106, Taiwan |
References:
[1] |
H. S. Bhat and R. C. Fetecau, A Hamiltonian regularization of the Burgers equation, J. Nonlinear Sci., 16 (2006), 615-638.
doi: 10.1007/s00332-005-0712-7. |
[2] |
H. S. Bhat and R. C. Fetecau, The Riemann problem for the Leray-Burgers equation, J. Differential Equations, 246 (2009), 3957-3979.
doi: 10.1016/j.jde.2009.01.006. |
[3] |
R. Camassa, Characteristics and initial value problem of a completely integrable shallow water equation, Discrete Contin. Dyn. Syst. Ser. B, 3 (2003), 115-139. |
[4] |
R. Camassa, J. Huang and L. Lee, On a completely integral numerical scheme for a nonlinear shallow-water wave equation, J. Nonlin. Math. Phys., 12 (2005), 146-162. |
[5] |
R. Camassa, J. Huang and L. Lee, Integral and integrable algorithm for a nonlinear shallow-water wave equation, J. Comp. Phys., 216 (2006), 547-572.
doi: 10.1016/j.jcp.2005.12.013. |
[6] |
R. Camassa, P. H. Chiu, L. Lee and T. W. H. Sheu, Viscous and inviscid regularizations in a class of evolutionary partial differential equations, J. Comp. Phys., 229 (2010), 6676-6687.
doi: 10.1016/j.jcp.2010.06.002. |
[7] |
A. Degasperis, D. D. Holm and A. N. W. Hone, Integrable and non-integrable equations with peakons, in "Nonlinear Physics: Theory and Experiment, II'' (Gallipoli, 2002), World Sci Publishing, River Edge, NJ, (2003), 37-43. |
[8] |
H. Holden and X. Raynaud, A convergent numerical scheme for the Camassa-Holm equation based on multipeakons, Discrete Contin. Dyn. Syst., 14 (2006), 505-528. |
[9] |
H. Holden and X. Raynaud, Convergence of a finite difference scheme for the Camassa-Holm equation, SIAM J. Numer. Anal., 44 (2006), 1655-1680.
doi: 10.1137/040611975. |
[10] |
J. Leray, Essai sur le mouvement d'un fluid visqueux emplissant l'space, Acat Math., 63 (1934), 93-258. |
[11] |
K. Mohseni, H. Zhao and J. Marsden, Shock regularization for the Burgers equation, AIAA Paper 2006-1516, 44th AIAA Aerospace Science Meeting and Exibit Reno, Nevada, Jan, 9-12, 2006. |
[12] |
G. Norgard and K. Mohseni, A regularization of the Burgers equation using a filtered convective velocity, J. Phys. A: Math. Theor., 41 (2008), 344016, 21pp.
doi: 10.1088/1751-8113/41/34/344016. |
show all references
References:
[1] |
H. S. Bhat and R. C. Fetecau, A Hamiltonian regularization of the Burgers equation, J. Nonlinear Sci., 16 (2006), 615-638.
doi: 10.1007/s00332-005-0712-7. |
[2] |
H. S. Bhat and R. C. Fetecau, The Riemann problem for the Leray-Burgers equation, J. Differential Equations, 246 (2009), 3957-3979.
doi: 10.1016/j.jde.2009.01.006. |
[3] |
R. Camassa, Characteristics and initial value problem of a completely integrable shallow water equation, Discrete Contin. Dyn. Syst. Ser. B, 3 (2003), 115-139. |
[4] |
R. Camassa, J. Huang and L. Lee, On a completely integral numerical scheme for a nonlinear shallow-water wave equation, J. Nonlin. Math. Phys., 12 (2005), 146-162. |
[5] |
R. Camassa, J. Huang and L. Lee, Integral and integrable algorithm for a nonlinear shallow-water wave equation, J. Comp. Phys., 216 (2006), 547-572.
doi: 10.1016/j.jcp.2005.12.013. |
[6] |
R. Camassa, P. H. Chiu, L. Lee and T. W. H. Sheu, Viscous and inviscid regularizations in a class of evolutionary partial differential equations, J. Comp. Phys., 229 (2010), 6676-6687.
doi: 10.1016/j.jcp.2010.06.002. |
[7] |
A. Degasperis, D. D. Holm and A. N. W. Hone, Integrable and non-integrable equations with peakons, in "Nonlinear Physics: Theory and Experiment, II'' (Gallipoli, 2002), World Sci Publishing, River Edge, NJ, (2003), 37-43. |
[8] |
H. Holden and X. Raynaud, A convergent numerical scheme for the Camassa-Holm equation based on multipeakons, Discrete Contin. Dyn. Syst., 14 (2006), 505-528. |
[9] |
H. Holden and X. Raynaud, Convergence of a finite difference scheme for the Camassa-Holm equation, SIAM J. Numer. Anal., 44 (2006), 1655-1680.
doi: 10.1137/040611975. |
[10] |
J. Leray, Essai sur le mouvement d'un fluid visqueux emplissant l'space, Acat Math., 63 (1934), 93-258. |
[11] |
K. Mohseni, H. Zhao and J. Marsden, Shock regularization for the Burgers equation, AIAA Paper 2006-1516, 44th AIAA Aerospace Science Meeting and Exibit Reno, Nevada, Jan, 9-12, 2006. |
[12] |
G. Norgard and K. Mohseni, A regularization of the Burgers equation using a filtered convective velocity, J. Phys. A: Math. Theor., 41 (2008), 344016, 21pp.
doi: 10.1088/1751-8113/41/34/344016. |
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