Updated on 2021/12/25

OSHITA Yoshihito

Organization
Faculty of Natural Science and Technology Professor

### Degree

• Doctor(Mathematical Science) ( The University of Tokyo )

• Master(Mathematical Science) ( The University of Tokyo )

### Research Interests

• Nonlinear Partial Differential Equations

• 非線形偏微分方程式

### Research Areas

• Natural Science / Basic mathematics

• Natural Science / Applied mathematics and statistics

### Education

• 東京大学大学院   数理科学研究科   数理科学

- 2002

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Country： Japan

### Professional Memberships

• 日本応用数理学会

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• the Mathematical Society of Japan

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• 日本数学会

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• the Mathematical Society of Japan

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• SIAM: Society for Industrial and Applied Mathematics

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### Papers

• A rigorous derivation of mean-field models describing 2D micro phase separation Reviewed International coauthorship International journal

Barbara Niethammer, Yoshihito Oshita

Calculus of Variations and Partial Differential Equations   59 ( 2 )   2020.4

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Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC

<title>Abstract</title>We study the free boundary problem describing the micro phase separation of diblock copolymer melts in the regime that one component has small volume fraction <inline-formula><alternatives><tex-math>$$\rho$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ρ</mml:mi></mml:math></alternatives></inline-formula> such that the micro phase separation results in an ensemble of small disks of one component. We consider the two dimensional case in this paper, whereas the three dimensional case was already considered in Niethammer and Oshita (Calc Var PDE 39:273–305, 2010). Starting from the free boundary problem restricted to disks we rigorously derive the heterogeneous mean-field equations on a time scale of the order of <inline-formula><alternatives><tex-math>$${\mathcal {R } }^{3}\ln (1/\rho )$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup><mml:mo>ln</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>, where <inline-formula><alternatives><tex-math>$${\mathcal {R } }$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math></alternatives></inline-formula> is the mean radius of disks. On this time scale, the evolution is dominated by coarsening and stabilization of the radii of the disks, whereas migration of disks becomes only relevant on a larger time scale.

• A rigorous derivation of mean-field models for diblock copolymer melts Reviewed

Barbara Niethammer, Yoshihito Oshita

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS   39 ( 3-4 )   273 - 305   2010.11

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER

We study the free boundary problem describing the micro phase separation of diblock copolymer melts in the regime that one component has small volume fraction such that micro phase separation results in an ensemble of small balls of one component. Mean-field models for the evolution of a large ensemble of such spheres have been formally derived in Glasner and Choksi (Physica D, 238:1241-1255, 2009), Helmers et al. (Netw Heterog Media, 3(3):615-632, 2008). It turns out that on a time scale of the order of the average volume of the spheres, the evolution is dominated by coarsening and subsequent stabilization of the radii of the spheres, whereas migration becomes only relevant on a larger time scale. Starting from the free boundary problem restricted to balls we rigorously derive the mean-field equations in the early time regime. Our analysis is based on passing to the homogenization limit in the variational framework of a gradient flow.

• Multi-bump standing waves with critical frequency for nonlinear Schrodinger equations Reviewed International coauthorship International journal

Jaeyoung Byeon, Yoshihito Oshita

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE   27 ( 4 )   1121 - 1152   2010.7

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：GAUTHIER-VILLARS/EDITIONS ELSEVIER

We glue together standing wave solutions concentrating around critical points of the potential V with different energy scales. We devise a hybrid method using simultaneously a Lyapunov-Schmidt reduction method and a variational method to glue together standing waves concentrating on local minimum points which possibly have no corresponding limiting equations and those concentrating on general critical points which converge to solutions of corresponding limiting problems satisfying a non-degeneracy condition. (C) 2010 Elsevier Masson SAS. All rights reserved.

• Uniqueness of standing waves for nonlinear Schrdinger equations Reviewed

Jaeyoung Byeon, Yoshihito Oshita

Proceedings of the Royal Society of Edinburgh Section A: Mathematics   138 ( 5 )   975 - 987   2008.10

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For m &gt
0 and p ∈ (1, (N + 2)/(N - 2)), we show the uniqueness and a linearized non-degeneracy of solutions for the following problem: δu - |x|mu + up = 0, u &gt
0 in ℝN and lim |x|→∞ u(x) = 0. © 2008 The Royal Society of Edinburgh.

• An application of the modular function in nonlocal variational problems Reviewed

Xinfu Chen, Yoshihito Oshita

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS   186 ( 1 )   109 - 132   2007.10

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER

Using the modular function and its invariance under the action of a modular group and an heuristic reduction of a mathematical model, we present a mathematical account of a hexagonal pattern selection observed in di-block copolymer melts.

• Singular limit problem for some elliptic systems Reviewed

Yoshihito Oshita

SIAM JOURNAL ON MATHEMATICAL ANALYSIS   38 ( 6 )   1886 - 1911   2007

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SIAM PUBLICATIONS

For the sharp interface problem arising in the singular limit of some elliptic systems, we prove the existence and the nondegeneracy of solutions whose interface is a distorted circle in a two-dimensional bounded domain without any assumption on the symmetry of the domain.

• Periodicity and uniqueness of global minimizers of an energy functional containing a long-range interaction Reviewed

XF Chen, Y Oshita

SIAM JOURNAL ON MATHEMATICAL ANALYSIS   37 ( 4 )   1299 - 1332   2005

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SIAM PUBLICATIONS

We consider, on an interval of arbitrary length, global minimizers of a class of energy functionals containing a small parameter epsilon and a long-range interaction. Such functionals arise from models for phase separation in diblock copolymers and from stationary solutions of FitzHugh-Nagumo systems. We show that every global minimizer is periodic with a period of order epsilon(1/3). Also, we identify the number of global minimizers and provide asymptotic expansions for the periods and global minimizers.

• Existence of multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations Reviewed

J Byeon, Y Oshita

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS   29 ( 11-12 )   1877 - 1904   2004

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：MARCEL DEKKER INC

For elliptic equations of the form epsilon2 Deltau - V(x)u + u(p) = 0, x epsilon R-N, where the potential V satisfies lim inf(\x\--&gt;infinity) V(x) &gt; inf(RN) V(x) = 0, we prove the existence of new kinds of solutions, corresponding to semi-classical standing waves for nonlinear Schrodinger equations, with several local maximum points whose local maximum values are of different scales with respect to epsilon --&gt; 0.

• Stable stationary patterns and interfaces arising in reaction-diffusion systems Reviewed

Y Oshita

SIAM JOURNAL ON MATHEMATICAL ANALYSIS   36 ( 2 )   479 - 497   2004

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SIAM PUBLICATIONS

We study reaction-diffusion systems with FitzHugh-Nagumo-type nonlinearity. We consider the rich structures of stable stationary solutions for two different parameter scalings with the corresponding limiting problems. We study the complex phase separation patterns and derive the stationary interface equation for the limiting problems.

• On stable nonconstant stationary solutions and mesoscopic patterns for FitzHugh-Nagumo equations in higher dimensions Reviewed

Y Oshita

JOURNAL OF DIFFERENTIAL EQUATIONS   188 ( 1 )   110 - 134   2003.2

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE

FitzHugh-Nagumo equation has been studied extensively in the field of mathematical biology. It has the mechanism of "lateral inhibition" which seems to play a big role in the pattern formation of plankton distribution. We consider FitzHugh-Nagumo equation in high dimension and show the existence of stable nonconstant stationary solutions which have fine structures on a mesoscopic scale. We construct spatially periodic stationary solutions. Moreover, we compute the singular limit energy, which suggests that the transition from planar structure to droplet pattern can occur when parameters change. (C) 2002 Elsevier Science (USA). All rights reserved.

• Linear stability of radially symmetric equilibrium solutions to the singular limit problem of three-component activator-inhibitor model Reviewed

Takuya KOJIMA, Yoshihito OSHITA

Mathematical Journal of Okayama University   63   201 - 217   2021.1

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Language：English   Publishing type：Research paper (scientific journal)

• Blowup and global existence of a solution to a semilinear reaction-diffusion system with the fractional Laplacian Reviewed

Tomoyuki KAKEHI, Yoshihito OSHITA

Mathematical Journal of Okayama University   59   175 - 218   2017.1

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• STANDING WAVE CONCENTRATING ON COMPACT MANIFOLDS FOR NONLINEAR SCHRODINGER EQUATIONS Reviewed International coauthorship International journal

Jaeyoung Byeon, Ohsang Kwon, Yoshihito Oshita

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS   14 ( 3 )   825 - 842   2015.5

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER INST MATHEMATICAL SCIENCES

For k = 1, ... , K, let M-k be a q(k)-dimensional smooth compact framed manifold in R-N with q(k) epsilon {1, ... , N - 1}. We consider the equation -epsilon(2) Delta u + V(x)u - u(p) = 0 in R-N where for each k epsilon {1, ... , K} and some m(k) &gt; 0; V (x) = |dist(x, M-k)|(mk) + O(|dist(x, M-k)|(mk+1)) as dist( x, M-k) -&gt; 0. For a sequence of epsilon converging to zero, we will find a positive solution u(epsilon) of the equation which concentrates on M-1 boolean OR ... boolean OR M-K.

• Gradient flow structure of mean-field models for micro phase separation Reviewed

Y. Oshita

RIMS Kôkyûroku Bessatsu   B31   13 - 29   2012

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### MISC

• 活性因子・抑制因子型反応拡散系の特異摂動問題とパターン形成 Reviewed

大下承民

応用数理   17 (3) 215-226   2007

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• Reduced rescaled problem of some activator-inhibitor systems

大下承民

数理解析研究所講究録   1498, 11-25   2006

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• Fine patterns arising in reaction-diffusion systems and Young measure

大下承民

数理解析研究所講究録   1416, 1-11   2005

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• 反応拡散系に現れる微細なパターンと Young 測度

大下承民

物性研究   84,79-96   2005

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• Fine structures arising in reaction-diffusion equations

大下承民

Trends in Mathematics   8, 77-80   2005

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• FitzHugh-Nagumo 方程式に現れる微細パターンについて

大下承民

数理解析研究所講究録   1356, 82-90   2004

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• Stable pattern of FitzHugh-Nagumo equation for higher dimensions and its limiting problem.

大下承民

数理解析研究所講究録   1237, 174-193   2001

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• Multiple solutions of boundary value problems for semilinear wave equations.

大下承民

数理解析研究所講究録   1076, 65-82   1999

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### Presentations

• Singular limit problem for some elliptic systems

碩学特別講演会  2008

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• Hexagonal Patterns of Di-Block Copolymer Melts

SIAM Conference on Mathematical Aspects of Materials Science  2008

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• Existence of multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations

Variational Methods for Elliptic PDE's and Hamiltonian Systems  2008

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• Uniqueness of standing waves for nonlinear Schrodinger equations

Young Asian Conference on Partial Differential Equations  2008

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• Singular limit problems for some elliptic systems

SIAM Conference on Analysis of Partial Differential Equations (PD07)  2007

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• 反応拡散系の特異摂動問題

数学教室談話会  2006

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• Singular limit problem for some elliptic systems

変分問題とその周辺  2006

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• 楕円型方程式系の特異極限問題

日本数学会  2006

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• 反応拡散系に現れる微細なパターンの構造

Workshop on Phenomena and its Structures  2005

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• 反応拡散系に現れる微細な構造

NSC セミナー  2005

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• 反応拡散系に現れる微細なパターンとYoung 測度

日本数学会 函数方程式論分科会 特別講演  2005

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• Fine structures arising in reaction-diffusion equations,

The 7th international workshop on differential equations  2005

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• 反応拡散系の特異極限問題について

名古屋微分方程式セミナー  2005

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• activator-inhibitor 系における水玉パターンの構成

解析セミナー  2005

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• activator-inhibitor 系の特異極限問題に対する空間周期的定常解

偏微分方程式セミナー  2005

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• Spatially periodic steady states for singular limiting problem of activator-inhibitor systems

Asymptotic analysis and singularity, MSJ-IRI 2005,  2005

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• Distortion of spots arising in activator-inhibitor system，

Conference on nonlinear elliptic and parabolic partial differential equations  2005

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• 反応拡散系に現れる微細構造について,

応用数理サマーセミナー  2005

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• Spot steady states of the reduced rescaled activator-inhibitor system,

SNU-HU 3rd Joint symposium on mathematics  2005

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• Distorted spots arising in activator-inhibitor systems，

Mathematical analysis of complex phenomena in life sciences,  2005

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• Reduced rescaled problem of some activator-inhibitor systems,

反応拡散系に現れる時・空間パターンのメカニズム  2005

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• Distroted spots arising in activator-inhibitor systems

応用数学合同研究集会  2005

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• Existence of multi-bump standing waves with a critical frequency for nonlinear Schrodinger eqauations

日本数学会  2004

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• Fine structures arising in FitzHugh-Nagumo equations

日本数学会  2004

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• Multi-bump standing waves with a critical frequency for nonlinear Schroedinger equations,

変分セミナー  2004

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• Nondegeneracy conditions of positive solutions of nonlinear elliptic equations and its applications to multi-bump solutions

2004

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• Fine structure arising in some activator-inhibitor system in 2-dimension space,

2004

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• Young measure on fine structures of some reaction-diffusion systems

反応拡散系に現れる時・空間パターンのメカニズム  2004

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• Young measure on fine structures of some reaction-diffusion systems,

Workshop on Singularities arising in Nonlinear Problems (SNP2004)  2004

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• Fine structures arising in reaction-diffusion systems and Young measure,

非線形数理「冬の学校」  2004

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• Stable stationary patterns and interfaces arising in reaction-diffusion systems

Workshop on complex patterns of solutions for nonlinear elliptic problems,  2003

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• Fine structures arising in FitzHugh-Nagumo equations

Pattern formation and asymptotic geometric structure in reaction-diffusion systems  2003

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• Stable patterns with fine structures arising in FitzHugh-Nagumo equations

Mathematical understanding of complex patterns in the life sciences  2003

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• Applications of modular functions to periodic dotted interfacial patterns

New perspectives of nonlinear partial differential equations  2003

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### Class subject in charge

• Literacy for Scientists （2021academic year） special  - その他

• A Basic Course in Calculus I （2021academic year） 1st and 2nd semester  - 水1,水2

• Basic Course in Calculus I （2021academic year） 1st and 2nd semester  - 水1～2

• Basic Course in Calculus Ia （2021academic year） 1st semester  - 水1,水2

• Basic Course in Calculus Ib （2021academic year） Second semester  - 水1,水2

• Real Analysis （2021academic year） Late  - 木5,木6

• Elementary　Information　Processing （2021academic year） 3rd and 4th semester  - 月5,月6

• Elementary　Information　Processing　a （2021academic year） Third semester  - 月5,月6

• Elementary　Information　Processing　b （2021academic year） Fourth semester  - 月5,月6

• Basic Analysis A （2021academic year） 3rd and 4th semester  - 木3,木4

• Basic Analysis Aa （2021academic year） Third semester  - 木3,木4

• Basic Analysis Ab （2021academic year） Fourth semester  - 木3,木4

• Seminar in Analysis （2021academic year） Year-round  - その他

• Advanced Analysis I （2021academic year） 1st and 2nd semester  - 月3,月4

• Nonlinear Partial Differential Equation （2021academic year） Late  - その他

• Literacy for Scientists （2020academic year） special  - その他

• Real Analysis （2020academic year） Late  - 木5,木6

• Basic Geometry A （2020academic year） 1st and 2nd semester  - 木3,木4

• Basic Geometry Aa （2020academic year） 1st semester  - 木3,木4

• Excercises in Basic Geometry Aa （2020academic year） 1st semester  - 木5,木6

• Basic Geometry Ab （2020academic year） Second semester  - 木3,木4

• Excercises in Basic Geometry Ab （2020academic year） Second semester  - 木5,木6

• Excercises in Basic Geometry A （2020academic year） 1st and 2nd semester  - 木5,木6

• Glance at Mathematical Science C （2020academic year） Third semester  - 金5,金6

• Basic Analysis A （2020academic year） 3rd and 4th semester  - 木3,木4

• Basic Analysis Aa （2020academic year） Third semester  - 木3,木4

• Basic Analysis Ab （2020academic year） Fourth semester  - 木3,木4

• Seminar in Analysis （2020academic year） Year-round  - その他

• Advanced Analysis I （2020academic year） 1st and 2nd semester  - 月3,月4