Behavior of radially symmetric solutions for a free boundary problem related to cell motility

Previous Article
Multiphase volume-preserving interface motions via localized signed distance vector scheme
DCDS-S Home
This Issue
Next Article
A Lotka-Volterra system with patch structure (related to a multi-group SI epidemic model)

2015, 8(5): 989-997. doi: 10.3934/dcdss.2015.8.989

Behavior of radially symmetric solutions for a free boundary problem related to cell motility

1.	Meiji Institute of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, 164-8525

Received December 2013 Revised June 2014 Published July 2015

Abstract
Related Papers

We consider a free boundary problem related to cell motility. In the previous work, the author [5] replaced the boundary condition, in the original problem, with a simple boundary condition and studied the behavior of radially symmetric solutions for the modified problem. In this paper, we consider the original mathematical model and show that the behavior of solutions for the model is similar to the one of solutions for the modified model under the certain condition.

Keywords: Free boundary problems, cell crawling..

Mathematics Subject Classification: Primary: 35R35; Secondary: 92C1.

Citation: Harunori Monobe. Behavior of radially symmetric solutions for a free boundary problem related to cell motility. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 989-997. doi: 10.3934/dcdss.2015.8.989

References:

[1]	G. M. Lieberman, Second Order Parabolic Differential Equations,, World. Scientific, (1996). doi: 10.1142/3302.
[2]	A. Mogilner and B. Rubinstein et al, Actin-myosin viscoelastic flow in the keratocyte lamellipod,, Bio. J., 97 (2009), 1853.
[3]	A. Mogilner, J. Stajic and C. W. Wolgemuth, Redundant mechanisms for stable cell locomotion revealed by minimal models,, Biophys J., 101 (2011), 545.
[4]	A. Mogilner and D. W. Verzi, A simple 1-D physical model for the crawling nematode sperm cell,, J. Stat. Phys., 110 (2003), 1169.
[5]	H. Monobe, Behavior of solutions for a free boundary problem describing amoeba motion,, Differential and Integral Equations, 25 (2012), 93.
[6]	H. Monobe and N. Hirokazu, Multiple existence of traveling waves of a free boundary problem describing cell motility,, Discrete Contin. Dyn. Syst., 19 (2014), 789. doi: 10.3934/dcdsb.2014.19.789.
[7]	T. Umeda, A chemo-mechanical model for amoeboid cell movement,, (in preparation)., ().

show all references

References:

[1]	G. M. Lieberman, Second Order Parabolic Differential Equations,, World. Scientific, (1996). doi: 10.1142/3302.
[2]	A. Mogilner and B. Rubinstein et al, Actin-myosin viscoelastic flow in the keratocyte lamellipod,, Bio. J., 97 (2009), 1853.
[3]	A. Mogilner, J. Stajic and C. W. Wolgemuth, Redundant mechanisms for stable cell locomotion revealed by minimal models,, Biophys J., 101 (2011), 545.
[4]	A. Mogilner and D. W. Verzi, A simple 1-D physical model for the crawling nematode sperm cell,, J. Stat. Phys., 110 (2003), 1169.
[5]	H. Monobe, Behavior of solutions for a free boundary problem describing amoeba motion,, Differential and Integral Equations, 25 (2012), 93.
[6]	H. Monobe and N. Hirokazu, Multiple existence of traveling waves of a free boundary problem describing cell motility,, Discrete Contin. Dyn. Syst., 19 (2014), 789. doi: 10.3934/dcdsb.2014.19.789.
[7]	T. Umeda, A chemo-mechanical model for amoeboid cell movement,, (in preparation)., ().

[1]	Avner Friedman. Free boundary problems arising in biology. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 193-202. doi: 10.3934/dcdsb.2018013
[2]	Harunori Monobe, Hirokazu Ninomiya. Multiple existence of traveling waves of a free boundary problem describing cell motility. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 789-799. doi: 10.3934/dcdsb.2014.19.789
[3]	Avner Friedman. Free boundary problems for systems of Stokes equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1455-1468. doi: 10.3934/dcdsb.2016006
[4]	Serena Dipierro, Enrico Valdinoci. (Non)local and (non)linear free boundary problems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (3) : 465-476. doi: 10.3934/dcdss.2018025
[5]	Noriaki Yamazaki. Almost periodicity of solutions to free boundary problems. Conference Publications, 2001, 2001 (Special) : 386-397. doi: 10.3934/proc.2001.2001.386
[6]	Ugur G. Abdulla, Evan Cosgrove, Jonathan Goldfarb. On the Frechet differentiability in optimal control of coefficients in parabolic free boundary problems. Evolution Equations & Control Theory, 2017, 6 (3) : 319-344. doi: 10.3934/eect.2017017
[7]	Daniela De Silva, Fausto Ferrari, Sandro Salsa. On two phase free boundary problems governed by elliptic equations with distributed sources. Discrete & Continuous Dynamical Systems - S, 2014, 7 (4) : 673-693. doi: 10.3934/dcdss.2014.7.673
[8]	Huiqiang Jiang. Regularity of a vector valued two phase free boundary problems. Conference Publications, 2013, 2013 (special) : 365-374. doi: 10.3934/proc.2013.2013.365
[9]	Mingxin Wang. Existence and uniqueness of solutions of free boundary problems in heterogeneous environments. Discrete & Continuous Dynamical Systems - B, 2018, 22 (11) : 1-7. doi: 10.3934/dcdsb.2018179
[10]	Jesús Ildefonso Díaz. On the free boundary for quenching type parabolic problems via local energy methods. Communications on Pure & Applied Analysis, 2014, 13 (5) : 1799-1814. doi: 10.3934/cpaa.2014.13.1799
[11]	Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences. Inverse Problems & Imaging, 2016, 10 (4) : 869-898. doi: 10.3934/ipi.2016025
[12]	Noriaki Yamazaki. Doubly nonlinear evolution equations associated with elliptic-parabolic free boundary problems. Conference Publications, 2005, 2005 (Special) : 920-929. doi: 10.3934/proc.2005.2005.920
[13]	Pierangelo Ciurlia. On a general class of free boundary problems for European-style installment options with continuous payment plan. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1205-1224. doi: 10.3934/cpaa.2011.10.1205
[14]	Joachim Escher, Christina Lienstromberg. A survey on second order free boundary value problems modelling MEMS with general permittivity profile. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 745-771. doi: 10.3934/dcdss.2017038
[15]	Hayk Mikayelyan, Henrik Shahgholian. Convexity of the free boundary for an exterior free boundary problem involving the perimeter. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1431-1443. doi: 10.3934/cpaa.2013.12.1431
[16]	Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. I. Well-posedness and convergence of the method of lines. Inverse Problems & Imaging, 2013, 7 (2) : 307-340. doi: 10.3934/ipi.2013.7.307
[17]	Toyohiko Aiki. A free boundary problem for an elastic material. Conference Publications, 2007, 2007 (Special) : 10-17. doi: 10.3934/proc.2007.2007.10
[18]	Borys V. Bazaliy, Ya. B. Bazaliy, Avner Friedman, Bei Hu. Energy Considerations in a Model of Nematode Sperm Crawling. Mathematical Biosciences & Engineering, 2006, 3 (2) : 347-370. doi: 10.3934/mbe.2006.3.347
[19]	Xinfu Chen, Huibin Cheng. Regularity of the free boundary for the American put option. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1751-1759. doi: 10.3934/dcdsb.2012.17.1751
[20]	Xiaoshan Chen, Fahuai Yi. Free boundary problem of Barenblatt equation in stochastic control. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1421-1434. doi: 10.3934/dcdsb.2016003

2017 Impact Factor: 0.561

American Institute of Mathematical Sciences