-
Previous Article
Behavior of radially symmetric solutions for a free boundary problem related to cell motility
- DCDS-S Home
- This Issue
-
Next Article
Numerical algorithm for tracking cell dynamics in 4D biomedical images
Multiphase volume-preserving interface motions via localized signed distance vector scheme
1. | Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192, Japan |
2. | Institute of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192, Japan |
References:
[1] |
N. Aguilera, H. W. Alt and L. A. Caffarelli, An optimization problem with volume constraint,, SIAM J. Control and Optimization, 24 (1986), 191.
doi: 10.1137/0324011. |
[2] |
H. W. Alt, L. A. Caffarelli and A. Friedman, Variational prrblems with two phases and their free boundaries,, Trans. Amer. Math. Soc., 282 (1984), 431.
doi: 10.1090/S0002-9947-1984-0732100-6. |
[3] |
J. W. Barrett, H. Garcke and R. Nürnberg, Parametric approximation of willmore flow and related geometric evolution equations,, SIAM J. Sci. Comput., 31 (2008), 225.
doi: 10.1137/070700231. |
[4] |
G. Barles and C. Georgelin, A simple proof of convergence of an approximation scheme for computing motions by mean curvature,, SIAM J. Numer. Anal., 32 (1995), 484.
doi: 10.1137/0732020. |
[5] |
I. C. Dolcetta, S. F. Vita and R. March, Area preserving curve shortening flows: From phase separation to image processing,, Interfaces and Free Boundaries, 4 (2002), 325.
doi: 10.4171/IFB/64. |
[6] |
M. Elsey, S. Esedoglu and P. Smereka, Diffusion generated motion for grain growth in two and three dimensions,, J. Comp. Physics, 228 (2009), 8015.
doi: 10.1016/j.jcp.2009.07.020. |
[7] |
S. Esedoglu, S. Ruuth and R. Tsai, Diffusion-generated motion using signed distance functions,, J. Comp. Physics, 229 (2010), 1017.
doi: 10.1016/j.jcp.2009.10.002. |
[8] |
L. Evans, Convergence of an algorithm for mean curvature motion,, Indiana University Mathematics Journal, 42 (1993), 533.
doi: 10.1512/iumj.1993.42.42024. |
[9] |
M. Gage, Curve shortening makes convex curves circular,, Invent. Math., 76 (1984), 357.
doi: 10.1007/BF01388602. |
[10] |
E. Ginder, S. Omata and K. Švadlenka, A variational method for diffusion-generated area-preserving interface motion,, Theoretical and Applied Mechanics Japan, 60 (2011), 265. Google Scholar |
[11] |
E. Ginder, A Variational Approach to Volume-Controlled Evolutionary Equations,, PhD Thesis, (2013). Google Scholar |
[12] |
J. Hass, M. Hutchings and R. Schlafly, The double bubble conjecture,, Electron. Res. Announc. Amer. Math. Soc., 1 (1995), 98.
doi: 10.1090/S1079-6762-95-03001-0. |
[13] |
K. Ishii, Mathematical analysis to an approximation scheme for mean curvature flow,, in International Symposium on Computational Science 2011 (eds. S. Omata and K. Svadlenka), 34 (2011), 67.
|
[14] |
B. Merriman, J. Bence and S. Osher, Motion of multiple junctions: A level set approach,, J. Comp. Physics, 112 (1994), 334.
doi: 10.1006/jcph.1994.1105. |
[15] |
R. Z. Mohammad and K. Švadlenka, On a penalization method for an evolutionary free boundary problem with volume constraint,, Adv. Math. Sci. Appl., 24 (2014), 85. Google Scholar |
[16] |
E. Rothe, Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben,, Math. Ann., 102 (1930), 650.
doi: 10.1007/BF01782368. |
[17] |
S. Ruuth and B. Wetton, A simple scheme for volume-preserving motion by mean curvature,, J. Scientific Computing, 19 (2003), 373.
doi: 10.1023/A:1025368328471. |
[18] |
K. Švadlenka, E. Ginder and S. Omata, A variational method for multiphase area-preserving interface motions,, J. Comp. Appl. Math, 257 (2014), 157.
doi: 10.1016/j.cam.2013.08.027. |
[19] |
P. Tilli, On a constrained variational problem with an arbitrary number of free boundaries,, Interfaces Free Bound, 2 (2000), 201.
doi: 10.4171/IFB/18. |
[20] |
H.-K. Zhao, B. Merriman, S. Osher and L. Wang, Capturing the behavior of bubbles and drops using the variational level set approach,, J. Comp. Phys., 143 (1998), 495.
doi: 10.1006/jcph.1997.5810. |
show all references
References:
[1] |
N. Aguilera, H. W. Alt and L. A. Caffarelli, An optimization problem with volume constraint,, SIAM J. Control and Optimization, 24 (1986), 191.
doi: 10.1137/0324011. |
[2] |
H. W. Alt, L. A. Caffarelli and A. Friedman, Variational prrblems with two phases and their free boundaries,, Trans. Amer. Math. Soc., 282 (1984), 431.
doi: 10.1090/S0002-9947-1984-0732100-6. |
[3] |
J. W. Barrett, H. Garcke and R. Nürnberg, Parametric approximation of willmore flow and related geometric evolution equations,, SIAM J. Sci. Comput., 31 (2008), 225.
doi: 10.1137/070700231. |
[4] |
G. Barles and C. Georgelin, A simple proof of convergence of an approximation scheme for computing motions by mean curvature,, SIAM J. Numer. Anal., 32 (1995), 484.
doi: 10.1137/0732020. |
[5] |
I. C. Dolcetta, S. F. Vita and R. March, Area preserving curve shortening flows: From phase separation to image processing,, Interfaces and Free Boundaries, 4 (2002), 325.
doi: 10.4171/IFB/64. |
[6] |
M. Elsey, S. Esedoglu and P. Smereka, Diffusion generated motion for grain growth in two and three dimensions,, J. Comp. Physics, 228 (2009), 8015.
doi: 10.1016/j.jcp.2009.07.020. |
[7] |
S. Esedoglu, S. Ruuth and R. Tsai, Diffusion-generated motion using signed distance functions,, J. Comp. Physics, 229 (2010), 1017.
doi: 10.1016/j.jcp.2009.10.002. |
[8] |
L. Evans, Convergence of an algorithm for mean curvature motion,, Indiana University Mathematics Journal, 42 (1993), 533.
doi: 10.1512/iumj.1993.42.42024. |
[9] |
M. Gage, Curve shortening makes convex curves circular,, Invent. Math., 76 (1984), 357.
doi: 10.1007/BF01388602. |
[10] |
E. Ginder, S. Omata and K. Švadlenka, A variational method for diffusion-generated area-preserving interface motion,, Theoretical and Applied Mechanics Japan, 60 (2011), 265. Google Scholar |
[11] |
E. Ginder, A Variational Approach to Volume-Controlled Evolutionary Equations,, PhD Thesis, (2013). Google Scholar |
[12] |
J. Hass, M. Hutchings and R. Schlafly, The double bubble conjecture,, Electron. Res. Announc. Amer. Math. Soc., 1 (1995), 98.
doi: 10.1090/S1079-6762-95-03001-0. |
[13] |
K. Ishii, Mathematical analysis to an approximation scheme for mean curvature flow,, in International Symposium on Computational Science 2011 (eds. S. Omata and K. Svadlenka), 34 (2011), 67.
|
[14] |
B. Merriman, J. Bence and S. Osher, Motion of multiple junctions: A level set approach,, J. Comp. Physics, 112 (1994), 334.
doi: 10.1006/jcph.1994.1105. |
[15] |
R. Z. Mohammad and K. Švadlenka, On a penalization method for an evolutionary free boundary problem with volume constraint,, Adv. Math. Sci. Appl., 24 (2014), 85. Google Scholar |
[16] |
E. Rothe, Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben,, Math. Ann., 102 (1930), 650.
doi: 10.1007/BF01782368. |
[17] |
S. Ruuth and B. Wetton, A simple scheme for volume-preserving motion by mean curvature,, J. Scientific Computing, 19 (2003), 373.
doi: 10.1023/A:1025368328471. |
[18] |
K. Švadlenka, E. Ginder and S. Omata, A variational method for multiphase area-preserving interface motions,, J. Comp. Appl. Math, 257 (2014), 157.
doi: 10.1016/j.cam.2013.08.027. |
[19] |
P. Tilli, On a constrained variational problem with an arbitrary number of free boundaries,, Interfaces Free Bound, 2 (2000), 201.
doi: 10.4171/IFB/18. |
[20] |
H.-K. Zhao, B. Merriman, S. Osher and L. Wang, Capturing the behavior of bubbles and drops using the variational level set approach,, J. Comp. Phys., 143 (1998), 495.
doi: 10.1006/jcph.1997.5810. |
[1] |
Mohammad Safdari. The regularity of some vector-valued variational inequalities with gradient constraints. Communications on Pure & Applied Analysis, 2018, 17 (2) : 413-428. doi: 10.3934/cpaa.2018023 |
[2] |
Jiawei Chen, Shengjie Li, Jen-Chih Yao. Vector-valued separation functions and constrained vector optimization problems: optimality and saddle points. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-18. doi: 10.3934/jimo.2018174 |
[3] |
Dimitra Antonopoulou, Georgia Karali. A nonlinear partial differential equation for the volume preserving mean curvature flow. Networks & Heterogeneous Media, 2013, 8 (1) : 9-22. doi: 10.3934/nhm.2013.8.9 |
[4] |
Y. Goto, K. Ishii, T. Ogawa. Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature. Communications on Pure & Applied Analysis, 2005, 4 (2) : 311-339. doi: 10.3934/cpaa.2005.4.311 |
[5] |
Matteo Focardi. Vector-valued obstacle problems for non-local energies. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 487-507. doi: 10.3934/dcdsb.2012.17.487 |
[6] |
Markus Kunze, Abdallah Maichine, Abdelaziz Rhandi. Vector-valued Schrödinger operators in Lp-spaces. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1-13. doi: 10.3934/dcdss.2020086 |
[7] |
Zhangxin Chen. On the control volume finite element methods and their applications to multiphase flow. Networks & Heterogeneous Media, 2006, 1 (4) : 689-706. doi: 10.3934/nhm.2006.1.689 |
[8] |
Christiane Pöschl, Jan Modersitzki, Otmar Scherzer. A variational setting for volume constrained image registration. Inverse Problems & Imaging, 2010, 4 (3) : 505-522. doi: 10.3934/ipi.2010.4.505 |
[9] |
Changfeng Gui, Huaiyu Jian, Hongjie Ju. Properties of translating solutions to mean curvature flow. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 441-453. doi: 10.3934/dcds.2010.28.441 |
[10] |
Giulio Colombo, Luciano Mari, Marco Rigoli. Remarks on mean curvature flow solitons in warped products. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020153 |
[11] |
Nikos Katzourakis. Nonuniqueness in vector-valued calculus of variations in $L^\infty$ and some Linear elliptic systems. Communications on Pure & Applied Analysis, 2015, 14 (1) : 313-327. doi: 10.3934/cpaa.2015.14.313 |
[12] |
Olaf Klein. On the representation of hysteresis operators acting on vector-valued, left-continuous and piecewise monotaffine and continuous functions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (6) : 2591-2614. doi: 10.3934/dcds.2015.35.2591 |
[13] |
Emmanuel Hebey. The Lin-Ni's conjecture for vector-valued Schrödinger equations in the closed case. Communications on Pure & Applied Analysis, 2010, 9 (4) : 955-962. doi: 10.3934/cpaa.2010.9.955 |
[14] |
Luciano Abadías, Carlos Lizama, Pedro J. Miana, M. Pilar Velasco. On well-posedness of vector-valued fractional differential-difference equations. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2679-2708. doi: 10.3934/dcds.2019112 |
[15] |
Nikos Katzourakis. Corrigendum to the paper: Nonuniqueness in Vector-Valued Calculus of Variations in $ L^\infty $ and some Linear Elliptic Systems. Communications on Pure & Applied Analysis, 2019, 18 (4) : 2197-2198. doi: 10.3934/cpaa.2019098 |
[16] |
Asma Azaiez. Refined regularity for the blow-up set at non characteristic points for the vector-valued semilinear wave equation. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2397-2408. doi: 10.3934/cpaa.2019108 |
[17] |
Tobias H. Colding and Bruce Kleiner. Singularity structure in mean curvature flow of mean-convex sets. Electronic Research Announcements, 2003, 9: 121-124. |
[18] |
Edoardo Mainini. On the signed porous medium flow. Networks & Heterogeneous Media, 2012, 7 (3) : 525-541. doi: 10.3934/nhm.2012.7.525 |
[19] |
Nicolas Dirr, Federica Dragoni, Max von Renesse. Evolution by mean curvature flow in sub-Riemannian geometries: A stochastic approach. Communications on Pure & Applied Analysis, 2010, 9 (2) : 307-326. doi: 10.3934/cpaa.2010.9.307 |
[20] |
Yoshikazu Giga, Yukihiro Seki, Noriaki Umeda. On decay rate of quenching profile at space infinity for axisymmetric mean curvature flow. Discrete & Continuous Dynamical Systems - A, 2011, 29 (4) : 1463-1470. doi: 10.3934/dcds.2011.29.1463 |
2018 Impact Factor: 0.545
Tools
Metrics
Other articles
by authors
[Back to Top]