
Previous Article
Nonlinear Schrödinger equations with inversesquare potentials in two dimensional space
 PROC Home
 This Issue

Next Article
Absorbing boundary conditions for the Westervelt equation
Largetime behavior for a PDE model of isothermal grain boundary motion with a constraint
1.  Department of Mathematics, Faculty of Education, Chiba University, 133 Yayoicho, Inageku, Chiba, 2638522 
2.  Department of General Education, Salesian Polytechnic, 468 Oyamagaoka, Machidacity, Tokyo, 1940215 
References:
[1] 
M. Amar and G. Bellettini, A notion of total variation depending on a metric with discontinuous coefficients,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 11 (1994), 91. Google Scholar 
[2] 
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems,, Oxford Science Publications, (2000). Google Scholar 
[3] 
H. Attouch, G. Buttazzo and G. Michaille, Variational Analysis in Sobolev and BV Spaces,, Applications to PDEs and Optimization, (2001). Google Scholar 
[4] 
G. Dal Maso, An introduction to $\Gamma$convergence,, Progress in Nonlinear Differential Equations and their Applications, 8 (1993). Google Scholar 
[5] 
L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions,, Studies in Advanced Mathematics, (1992). Google Scholar 
[6] 
E. Giusti, Minimal Surfaces and Functions of Bounded Variation,, Monographs in Mathematics, 80 (1984). Google Scholar 
[7] 
R. Kobayashi, Modeling of grain structure evolution,, Variational Problems and Related Topics, 1210 (2001), 68. Google Scholar 
[8] 
J. S. Moll and K. Shirakawa, Existence of solutions to the KobayashiWarrenCarter system,, Calc. Var. Partial Differential Equations, 51 (2014), 3. Google Scholar 
[9] 
J. S. Moll, K. Shirakawa and H. Watanabe, Energy dissipative solutions to the KobayashiWarrenCarter system,, In preparation., (). Google Scholar 
[10] 
Ken Shirakawa and H. Watanabe, Energydissipative solution to a onedimensional phase field model of grain boundary motion,, Discrete Conin. Dyn. Syst. Ser. S, 7 (2014), 139. Google Scholar 
[11] 
K. Shirakawa, H. Watanabe and N. Yamazaki, Solvability of onedimensional phase field systems associated with grain boundary motion,, Math. Ann., 356 (2013), 301. Google Scholar 
[12] 
K. Shirakawa, H. Watanabe and N. Yamazaki, Existence for a PDEmodel of a grain boundary motion involving solidification effect,, New Role of the Theory of Abstract Evolution Equations, 1892 (2014), 52. Google Scholar 
[13] 
K. Shirakawa, H. Watanabe and N. Yamazaki, Phasefield systems for grain boundary motions under isothermal solidifications,, Adv. Math. Sci. Appl. (to appear)., (). Google Scholar 
[14] 
J. Simon, Compact sets in the space $ L^p(0,T;B) $,, Ann. Mat. Pura Appl. (4), 146 (1987), 65. Google Scholar 
[15] 
H. Watanabe and K. Shirakawa, Qualitative properties of a onedimensional phasefield system associated with grain boundary,, GAKUTO Internat. Ser. Math. Sci. Appl., 36 (2013), 301. Google Scholar 
[16] 
H. Watanabe and K. Shirakawa, Stability for approximation methods of the onedimensional KobayashiWarrenCarter system,, Math. Bohem., 139 (2014), 381. Google Scholar 
show all references
References:
[1] 
M. Amar and G. Bellettini, A notion of total variation depending on a metric with discontinuous coefficients,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 11 (1994), 91. Google Scholar 
[2] 
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems,, Oxford Science Publications, (2000). Google Scholar 
[3] 
H. Attouch, G. Buttazzo and G. Michaille, Variational Analysis in Sobolev and BV Spaces,, Applications to PDEs and Optimization, (2001). Google Scholar 
[4] 
G. Dal Maso, An introduction to $\Gamma$convergence,, Progress in Nonlinear Differential Equations and their Applications, 8 (1993). Google Scholar 
[5] 
L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions,, Studies in Advanced Mathematics, (1992). Google Scholar 
[6] 
E. Giusti, Minimal Surfaces and Functions of Bounded Variation,, Monographs in Mathematics, 80 (1984). Google Scholar 
[7] 
R. Kobayashi, Modeling of grain structure evolution,, Variational Problems and Related Topics, 1210 (2001), 68. Google Scholar 
[8] 
J. S. Moll and K. Shirakawa, Existence of solutions to the KobayashiWarrenCarter system,, Calc. Var. Partial Differential Equations, 51 (2014), 3. Google Scholar 
[9] 
J. S. Moll, K. Shirakawa and H. Watanabe, Energy dissipative solutions to the KobayashiWarrenCarter system,, In preparation., (). Google Scholar 
[10] 
Ken Shirakawa and H. Watanabe, Energydissipative solution to a onedimensional phase field model of grain boundary motion,, Discrete Conin. Dyn. Syst. Ser. S, 7 (2014), 139. Google Scholar 
[11] 
K. Shirakawa, H. Watanabe and N. Yamazaki, Solvability of onedimensional phase field systems associated with grain boundary motion,, Math. Ann., 356 (2013), 301. Google Scholar 
[12] 
K. Shirakawa, H. Watanabe and N. Yamazaki, Existence for a PDEmodel of a grain boundary motion involving solidification effect,, New Role of the Theory of Abstract Evolution Equations, 1892 (2014), 52. Google Scholar 
[13] 
K. Shirakawa, H. Watanabe and N. Yamazaki, Phasefield systems for grain boundary motions under isothermal solidifications,, Adv. Math. Sci. Appl. (to appear)., (). Google Scholar 
[14] 
J. Simon, Compact sets in the space $ L^p(0,T;B) $,, Ann. Mat. Pura Appl. (4), 146 (1987), 65. Google Scholar 
[15] 
H. Watanabe and K. Shirakawa, Qualitative properties of a onedimensional phasefield system associated with grain boundary,, GAKUTO Internat. Ser. Math. Sci. Appl., 36 (2013), 301. Google Scholar 
[16] 
H. Watanabe and K. Shirakawa, Stability for approximation methods of the onedimensional KobayashiWarrenCarter system,, Math. Bohem., 139 (2014), 381. Google Scholar 
[1] 
Linlin Li, Bedreddine Ainseba. Largetime behavior of matured population in an agestructured model. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020195 
[2] 
Akio Ito, Nobuyuki Kenmochi, Noriaki Yamazaki. Global solvability of a model for grain boundary motion with constraint. Discrete & Continuous Dynamical Systems  S, 2012, 5 (1) : 127146. doi: 10.3934/dcdss.2012.5.127 
[3] 
Youshan Tao, Lihe Wang, ZhiAn Wang. Largetime behavior of a parabolicparabolic chemotaxis model with logarithmic sensitivity in one dimension. Discrete & Continuous Dynamical Systems  B, 2013, 18 (3) : 821845. doi: 10.3934/dcdsb.2013.18.821 
[4] 
Marco Di Francesco, Yahya Jaafra. Multiple largetime behavior of nonlocal interaction equations with quadratic diffusion. Kinetic & Related Models, 2019, 12 (2) : 303322. doi: 10.3934/krm.2019013 
[5] 
Zhong Tan, Yong Wang, Fanhui Xu. Largetime behavior of the full compressible EulerPoisson system without the temperature damping. Discrete & Continuous Dynamical Systems  A, 2016, 36 (3) : 15831601. doi: 10.3934/dcds.2016.36.1583 
[6] 
Jishan Fan, Fei Jiang. Largetime behavior of liquid crystal flows with a trigonometric condition in two dimensions. Communications on Pure & Applied Analysis, 2016, 15 (1) : 7390. doi: 10.3934/cpaa.2016.15.73 
[7] 
Shifeng Geng, Lina Zhang. Largetime behavior of solutions for the system of compressible adiabatic flow through porous media with nonlinear damping. Communications on Pure & Applied Analysis, 2014, 13 (6) : 22112228. doi: 10.3934/cpaa.2014.13.2211 
[8] 
Zhenhua Guo, Wenchao Dong, Jinjing Liu. Largetime behavior of solution to an inflow problem on the half space for a class of compressible nonNewtonian fluids. Communications on Pure & Applied Analysis, 2019, 18 (4) : 21332161. doi: 10.3934/cpaa.2019096 
[9] 
Rinaldo M. Colombo, Francesca Monti. Solutions with large total variation to nonconservative hyperbolic systems. Communications on Pure & Applied Analysis, 2010, 9 (1) : 4760. doi: 10.3934/cpaa.2010.9.47 
[10] 
Nobuyuki Kenmochi, Noriaki Yamazaki. Global attractor of the multivalued semigroup associated with a phasefield model of grain boundary motion with constraint. Conference Publications, 2011, 2011 (Special) : 824833. doi: 10.3934/proc.2011.2011.824 
[11] 
Ken Shirakawa, Hiroshi Watanabe. Energydissipative solution to a onedimensional phase field model of grain boundary motion. Discrete & Continuous Dynamical Systems  S, 2014, 7 (1) : 139159. doi: 10.3934/dcdss.2014.7.139 
[12] 
Cong He, Hongjun Yu. Large time behavior of the solution to the Landau Equation with specular reflective boundary condition. Kinetic & Related Models, 2013, 6 (3) : 601623. doi: 10.3934/krm.2013.6.601 
[13] 
Jerry L. Bona, Laihan Luo. Largetime asymptotics of the generalized BenjaminOnoBurgers equation. Discrete & Continuous Dynamical Systems  S, 2011, 4 (1) : 1550. doi: 10.3934/dcdss.2011.4.15 
[14] 
Shijin Deng. Large time behavior for the IBVP of the 3D Nishida's model. Networks & Heterogeneous Media, 2010, 5 (1) : 133142. doi: 10.3934/nhm.2010.5.133 
[15] 
Sören Bartels, Marijo Milicevic. Iterative finite element solution of a constrained total variation regularized model problem. Discrete & Continuous Dynamical Systems  S, 2017, 10 (6) : 12071232. doi: 10.3934/dcdss.2017066 
[16] 
Liyan Ma, Lionel Moisan, Jian Yu, Tieyong Zeng. A stable method solving the total variation dictionary model with $L^\infty$ constraints. Inverse Problems & Imaging, 2014, 8 (2) : 507535. doi: 10.3934/ipi.2014.8.507 
[17] 
Zhengmeng Jin, Chen Zhou, Michael K. Ng. A coupled total variation model with curvature driven for image colorization. Inverse Problems & Imaging, 2016, 10 (4) : 10371055. doi: 10.3934/ipi.2016031 
[18] 
Wei Wang, Ling Pi, Michael K. Ng. SaturationValue Total Variation model for chromatic aberration correction. Inverse Problems & Imaging, 2020, 14 (4) : 733755. doi: 10.3934/ipi.2020034 
[19] 
Feimin Huang, Yeping Li. Large time behavior and quasineutral limit of solutions to a bipolar hydrodynamic model with large data and vacuum. Discrete & Continuous Dynamical Systems  A, 2009, 24 (2) : 455470. doi: 10.3934/dcds.2009.24.455 
[20] 
Robert M. Strain, Keya Zhu. Largetime decay of the soft potential relativistic Boltzmann equation in $\mathbb{R}^3_x$. Kinetic & Related Models, 2012, 5 (2) : 383415. doi: 10.3934/krm.2012.5.383 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]