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Articles and Proceedings (English)

Journal articles with peer review

1. Xianjin Chen, Chiun-Chang Lee and Masashi Mizuno, Unified asymptotic analysis and numerical simulations of singularly perturbed linear differential equations under various nonlocal boundary effects, Communications in Mathematical Sciences, 22 (2024), 394--434. doi:10.4310/CMS.2024.v22.n2.a5 MR4699824
2. Takashi Kagaya, Masashi Mizuno, Keisuke Takasao, Long time behavior for a curvature flow of networks related to grain boundary motion with the effect of lattice misoriantations, accepted to The Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
3. Yekaterina Epshteyn, Chang Liu, Chun Liu, Masashi Mizuno, Local well-posedness of a nonlinear Fokker-Planck model, Nonlinearity, 36 (2023), 1890--1917. doi:10.1088/1361-6544/acb7c2 MR4506846
4. Chiun-Chang Lee, Masashi Mizuno, Sang-Hyuck Moon, On the uniqueness of linear convection-diffusion equations in large domains with integral boundary conditions, Comptes Rendus Mathématique. 361 (2023), 191--206. doi:10.5802/crmath.396 MR4538545
5. Yekaterina Epshteyn, Chang Liu, Chun Liu, Masashi Mizuno, Nonlinear inhomogeneous Fokker-Planck models: energetic-variational structures and long time behavior, Analysis and Applications, 20 (2022), 1295--1356. doi:10.1142/S0219530522400036 MR4506846
6. Yekaterina Epshteyn, Chun Liu, Masashi Mizuno, A stochastic model of grain boundary dynamics: A Fokker-Planck perspective, Mathematical Models and Methods in Applied Sciences, 32 (2022), 2189--2236. doi:10.1142/S021820252250052X MR4526584
7. Katayun Barmak, Anastasia Dunca, Yekaterina Epshteyn, Chun Liu, Masashi Mizuno, Grain Growth and the Effect of Different Time Scales, Research in Mathematics of Materials Science, 33--58, Springer, Cham, 2022. doi:10.1007/978-3-031-04496-0_2
8. Masashi Mizuno, Keisuke Takasao, A curve shortening equation with time-dependent mobility related to grain boundary motions, Interfaces and Free Boundaries. 23 (2021), 169--190. doi:10.4171/IFB/453 doi:10.4171/IFB/453(New Site) MR4292952
9. Yekaterina Epshteyn, Chun Liu, Masashi Mizuno, Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag, Communications in Mathematical Sciences, 19 (2021), 1403--1428. doi:10.4310/CMS.2021.v19.n5.a10 MR4283537
10. Yekaterina Epshteyn, Chun Liu, Masashi Mizuno, Motion of grain boundaries with dynamic lattice misorientations and with triple junctions drag, SIAM Journal on Mathematical Analysis, 53 (2021), 3072--3097. doi:10.1137/19M1265855 MR4263432
11. Masashi Mizuno and Keisuke Takasao, Gradient estimates for mean curvature flow with Neumann boundary conditions, NoDEA. Nonlinear Differential Equations and Applications, 24 (2017), Art. 32, 24pp. doi:10.1007/s00030-017-0457-7 MR3661017
12. Masashi Mizuno and Yoshihiro Tonegawa, Erratum to "Convergence of the Allen-Cahn equation with Neumann boundary conditions," SIAM Journal on Mathematical Analysis, 48 (2016), 3035--3036. doi:10.1137/16M1074059 MR3542008
13. Masashi Mizuno and Yoshihiro Tonegawa, Convergence of the Allen-Cahn equation with Neumann boundary conditions, SIAM Journal on Mathematical Analysis, 47 (2015), 1906--1932. doi:10.1137/140987808 MR3348119
14. Masashi Mizuno and Takayoshi Ogawa, Regularity and asymptotic behavior for the Keller-Segel system of degenerate type with critical nonlinearity, Journal of Mathematical Sciences, The University of Tokyo, 20 (2013), 375--433. MR3156987
15. Masashi Mizuno, H\"older estimates for solutions of the Cauchy problem for the porous medium equation with external forces, Manuscripta Mathematica, 141 (2013), 273--313. doi:10.1007/s00229-012-0572-z MR3024690
16. Masashi Mizuno, Remarks on H\"older continuity for solutions of the $p$-Laplace evolution equations, Journal of Mathematical Analysis and Applications, 382 (2011), 785--791. doi:10.1016/j.jmaa.2011.04.076 MR2810831
17. Masashi Mizuno, Harnack estimates for some nonlinear parabolic equation, Differential and Integral Equations, 21 (2008), 693--716. 10.57262/die/1356038619 MR2479688

Preprints

1. Yekaterina Epshteyn, Chun Liu, and Masashi Mizuno, Longtime Asymptotic Behavior of Nonlinear Fokker-Planck Type Equations with Periodic Boundary Conditions, arXiv:2404.05157

Proceedings without peer review

1. Masashi Mizuno and Keisuke Takasao, Gradient estimates for mean curvature flow with Neumann boundary conditions, in RIMS K\^oky\^uroku, Theory of evolution equations and applications to nonlinear problems, 2066 (2018), 35--45.
2. Masashi Mizuno and Yoshihiro Tonegawa, Convergence of the Allen-Cahn equation with Neumann boundary conditions, in RIMS K\^oky\^uroku, Regularity and Singularity for Partial Differential Equations with Conservation Laws, 1962 (2015), 10--16.
3. Masashi Mizuno and Takayoshi Ogawa, H\"older continuity for some degenerate parabolic equation and its application, in RIMS K\^oky\^uroku, Nonlinear evolution equations and mathematical modeling, 1693 (2010), 45--56.

Doctoral thesis

• H\"older regularity for solutions of non-linear degenerate parabolic equations, Tohoku University, 2010