Research keywords (2)：
非線形偏微分方程式
, Nonlinear Partial Differential Equations
Research theme for competitive and other funds (33)：
2024 - 2029 楕円型方程式の精密解析と定性理論の新展開
2023 - 2026 Singularity and structure of solutions to nonlinear elliptic partial differential equations
2019 - 2024 優臨界・臨界・劣臨界楕円型方程式の解構造の総合的研究
2020 - 2023 非線形放物型偏微分方程式における定常構造および自己相似性と解の挙動
2017 - 2021 Motion of curves and surfaces by curvature : numerical altorithm, regularity and singularity
2018 - 2020 非線形放物型偏微分方程式の解の特異性と定常問題
2016 - 2018 非線形放物型偏微分方程式における臨界指数と解の挙動
2012 - 2017 Systematic studies on the profile and behavior of solutions of partial differential equations
2012 - 2015 Studies on approximate problems, regularity and singularity for mean curvature flow
2008 - 2012 Analysis for nonlinear critical phenomena described by mean field equations
2008 - 2010 Self-similarity and singularity of solutions for nonlinear parabolic PDEs
2008 - 2010 Studies on approximation, regularity and singularity for mean curvature flow
2007 - 2010 New development of the qualitative theory of nonlinear parabolic and elliptic equations
2006 - 2009 On the Study of behavior of blowup solutions to a chemotaxis system in high dimensional domains
2005 - 2007 Research of "Algebraic methods on spectrums of boundary control systems and applications to nonlinear systems"
2005 - 2007 Self-similar structure and singularity of solutions for nonlinear parabolic partial differential equations
2005 - 2007 Analytical study for mean curvature flow by using an numerical algorithm
2004 - 2006 Research of Optimal Control and Inverse Problems for Nonlinear Evolution Equations
2003 - 2004 Research of "Algebraic and analytic methods in the spectrum for boundary control systems and numerical analysis"
2002 - 2004 放物型非線形問題における自己相似性と解構造
2002 - 2004 Asymptotic analysis of nonlinear ordinary differential equations and its applications
2001 - 2003 Structure of solutions to the system of equations describing chemotactic aggregation of cellular slime molds
2001 - 2003 Reseach on Optimal Control and Inverse Problems for Nonlinear Partial Differential Equations
2000 - 2001 Asymptotic analysis of ordinary differential equations, and its application to partial differential equations
1999 - 2000 Structure of solutions to Keller-Segel system
1999 - 2000 Theoretical and Numerical Research of Control Theory and Identification Problems for nonlinear parabolic and Hyperbolic Distributed parameter System
1998 - 1999 非線形放物型偏微分方程式の自己相似解
1998 - 1999 An algebraic method for boundary control systems of parabolic type
1997 - 1998 Qualitative studies of solutions to elliptic equations in unbounded domains
1997 - 1998 Theoretical and Numerical Research of Optimal Control and Inverse Problems for Nonlinear Elliptic and Hyperbolic Distributed Parameter Systems
1995 - 1995 非線形楕円型偏微分方程式に対する定性的理論
1994 - 1994 非線形楕円型偏微分方程式の定性的研究
1994 - 1994 ポテンシャル論的手法の非線形問題への応用
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Papers (61)：
Yasuhito Miyamoto, Yūki Naito. A bifurcation diagram of solutions to semilinear elliptic equations with general supercritical growth. Journal of Differential Equations. 2024. 406. 318-337
Yasuhito Miyamoto, Yūki Naito. Singular solutions for semilinear elliptic equations with general supercritical growth. Annali di Matematica Pura ed Applicata. 2023. 202. 1. 341-366
Yūki Naito. Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions. Journal of Differential Equations. 2021. 297. 144-174
Miyamoto Yasuhito, Naito Yuki. Structure of positive solutions for semilinear elliptic equations with supercritical growth (Shapes and other properties of the solutions of PDEs). 数理解析研究所講究録. 2016. 2006. 20-29
Naito Yuki. Conditional oscillation for second order linear differential equations (New Developments of Functional Equations in Mathematical Analysis). RIMS Kokyuroku. 2010. 1702. 65-70
NAITO Yuki, SENBA Takasi. Self-similar blow-up for a chemotaxis system in higher dimensional domains (Mathematical analysis on the self-organization and self-similarity). RIMS Kokyuroku Bessatsu. 2009. 15. 87-99
Naito Yuki, Sato Tokushi. Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent (Variational Problems and Related Topics). RIMS Kokyuroku. 2009. 1671. 91-95
Naito Yuki, Sato Tokushi. Positive solutions for semilinear elliptic equations involving Dirac measures(Functional Equations Based upon Phenomena). RIMS Kokyuroku. 2007. 1547. 114-119
