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Multiple existence of traveling waves of a free boundary problem describing cell motility
1. | Meiji Institute of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, 164-8525, Japan |
2. | School of Interdisciplinary Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, 164-8525 |
References:
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P. K. Brazhnik, Exact solutions for the kinematic model of autowaves in two-dimensional excitable media, Physica D, 94 (1996), 205-220.
doi: 10.1016/0167-2789(96)00042-5. |
[2] |
Y. S. Choi, J. Lee and R. Lui, Traveling wave solutions for a one-dimensional crawling nematode sperm cell model, J. Math. Biol., 49 (2004), 310-328.
doi: 10.1007/s00285-003-0255-1. |
[3] |
Y. S. Choi, P. Groulxb and R. Lui, Moving boundary problem for a one-dimensional crawling nematode sperm cell model, Nonlinear Analysis: Real World Appl., 6 (2005), 874-898.
doi: 10.1016/j.nonrwa.2004.11.005. |
[4] |
Y. S. Choi and R. Lui, Existence of traveling domain solutions for a two-dimensional moving boundary problem, Trans. A. M. S., 361 (2009), 4027-4044.
doi: 10.1090/S0002-9947-09-04562-0. |
[5] |
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, New York, 1998.
doi: 10.1007/978-3-642-61798-0. |
[6] |
J.-S. Guo, H. Ninomiya and J.-C. Tsai, Existence and uniqueness of stabilized propagation wave segments in wave front interaction model, Physica D, 239 (2010), 230-239.
doi: 10.1016/j.physd.2009.11.001. |
[7] |
A. Mogilner and L. Edelstein-Keshet, Regulation of actin dynamics in rapidly moving cells, A quantitative analysis. Biophys. J., 83 (2002), 1237-1258.
doi: 10.1016/S0006-3495(02)73897-6. |
[8] |
A. Mogilner, J. Stajic and C. W. Wolgemuth, Redundant mechanisms for stable cell locomotion revealed by minimal models, Biophys J., 101 (2011), 545-553. |
[9] |
A. Mogilner and B. Rubinstein et al, Actin-myosin viscoelastic flow in the keratocyte lamellipod, Bio. J., 97 (2009), 1853-1863. |
[10] |
A. Mogilner and D. W. Verzi, A simple 1-D physical model for the crawling nematode sperm cell, J. Stat. Phys., 110 (2003), 1169-1189. |
[11] |
H. Monobe, Behavior of solutions for a free boundary problem describing amoeba motion, Differential and Integral Equations, 25 (2012), 93-116. |
[12] |
J. V. Small, M. Herzog and K. Anderson, Actin filament organization in the fish keratocyte lamellipodium, J. Cell Biol., 129 (1995), 1275-1286.
doi: 10.1083/jcb.129.5.1275. |
[13] |
V. S. Zykov and K. Showalter, Wave front interaction model of stabilized propagation of chemical waves segments, Phys. Rev. Lett., 94 (2005), 068302. |
show all references
References:
[1] |
P. K. Brazhnik, Exact solutions for the kinematic model of autowaves in two-dimensional excitable media, Physica D, 94 (1996), 205-220.
doi: 10.1016/0167-2789(96)00042-5. |
[2] |
Y. S. Choi, J. Lee and R. Lui, Traveling wave solutions for a one-dimensional crawling nematode sperm cell model, J. Math. Biol., 49 (2004), 310-328.
doi: 10.1007/s00285-003-0255-1. |
[3] |
Y. S. Choi, P. Groulxb and R. Lui, Moving boundary problem for a one-dimensional crawling nematode sperm cell model, Nonlinear Analysis: Real World Appl., 6 (2005), 874-898.
doi: 10.1016/j.nonrwa.2004.11.005. |
[4] |
Y. S. Choi and R. Lui, Existence of traveling domain solutions for a two-dimensional moving boundary problem, Trans. A. M. S., 361 (2009), 4027-4044.
doi: 10.1090/S0002-9947-09-04562-0. |
[5] |
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, New York, 1998.
doi: 10.1007/978-3-642-61798-0. |
[6] |
J.-S. Guo, H. Ninomiya and J.-C. Tsai, Existence and uniqueness of stabilized propagation wave segments in wave front interaction model, Physica D, 239 (2010), 230-239.
doi: 10.1016/j.physd.2009.11.001. |
[7] |
A. Mogilner and L. Edelstein-Keshet, Regulation of actin dynamics in rapidly moving cells, A quantitative analysis. Biophys. J., 83 (2002), 1237-1258.
doi: 10.1016/S0006-3495(02)73897-6. |
[8] |
A. Mogilner, J. Stajic and C. W. Wolgemuth, Redundant mechanisms for stable cell locomotion revealed by minimal models, Biophys J., 101 (2011), 545-553. |
[9] |
A. Mogilner and B. Rubinstein et al, Actin-myosin viscoelastic flow in the keratocyte lamellipod, Bio. J., 97 (2009), 1853-1863. |
[10] |
A. Mogilner and D. W. Verzi, A simple 1-D physical model for the crawling nematode sperm cell, J. Stat. Phys., 110 (2003), 1169-1189. |
[11] |
H. Monobe, Behavior of solutions for a free boundary problem describing amoeba motion, Differential and Integral Equations, 25 (2012), 93-116. |
[12] |
J. V. Small, M. Herzog and K. Anderson, Actin filament organization in the fish keratocyte lamellipodium, J. Cell Biol., 129 (1995), 1275-1286.
doi: 10.1083/jcb.129.5.1275. |
[13] |
V. S. Zykov and K. Showalter, Wave front interaction model of stabilized propagation of chemical waves segments, Phys. Rev. Lett., 94 (2005), 068302. |
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