Research keywords (9)：
Discrete Morse Flow method
, Blow up technique
, De Giorgi class, regularity theory, H\"older estimate
, Gamma-convergence
, Minimizing movement method
, discrete Morse flow method
, Energy functional with the singularity
, minimizing movement
, gradient flow
Research theme for competitive and other funds (16)：
2022 - 2027 時間発展型積分微分方程式の変分解析
2018 - 2023 関数空間上の汎関数に対するエネルギー最大勾配曲線の統合的研究
2015 - 2018 Monotonicity estimates and local regularity and singularity for the p-harmonic flows
2012 - 2015 Regularity for the evolutionary p-Laplace operator and global existence of the p-harmonic map flows
2012 - 2014 Geometric measure theory and hyperbolic operators ant its numerical calculations
2009 - 2011 A regularity criterion for the harmonic map flows and asymptotic analysis for singularity
2006 - 2009 New topics for partial differential equations whose solution has singular sets
2005 - 2008 Analysis of Fracture Propagation in the problem of image segmentation
2004 - 2007 Research on Spectra of Perron-Frobenius operator generated by dynamical systm and random numbers
2003 - 2004 Study on Regularity and Singularity of Minimal Surfaces in Higher Dimensions and The Evolution
2002 - 2003 Research on Perron-Frobenius operator and fractals
2000 - 2001 Research on ergodic theory and Perron-Frobenius operator
1995 - 1996 Probabilistic investigation of phase transitions for lattice spin systems
1995 - 1995 幾何学的測度論及びその時間発展問題の研究
1994 - 1994 変分問題と大域解析学
1994 - 1994 液晶の数理解析
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Papers (19)：
Kato, N, Misawa, M, Nakamura, K, Yamaura, Y. Existence for doubly nonlinear fractional p-Laplacian equations. Annali di Matematica Pura ed Applicata. 2024
A volume constraint problem for the nonlocal doubly nonlinear parabolic equation. Mathematics in Engineering. 2023. 6. 6. 1-26
Yoshihiko Yamaura. A convergence of the approximated free boundary of regularized functionals via Gamma-convergence. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2008. 218. 2. 473-481
Yoshifumi Mimura, Yoshihiko Yamaura. Another interpretation for the Weissler's critical exponent in the theory of semilinear parbolic PDE. International Journal of Differential Equations and Applications. 2020. 19. 1. 109-132
Nobuyuki Kato, Masashi Misawa, Yoshihiko Yamaura. The discrete Morse flow method for parabolic p-Laplacian systems. Annali di Matematica Pura ed Applicata. 2020. 200. 3. 1245-1275
Yoshihiko Yamaura. A construction of a uniform continuous minimizing movement associated with a singular functional. RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA. 2017. 137. 155-184
Nobuyuki Kato, Yoshihiko Yamaura. Uniform Holder continuity of approximate solutions to parabolic systems and its application. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. 2017. 42. 1. 1-23
Construction of a more highly integrable weak solution to hyperbolic systems with coefficients satisfying the Legendre-Hadamard condition
(International workshop Regularity and Singularity for Geometric PDE and related topics 2024)
On a convergence for the approximation of the gradient flow curve to the non-convex and singular functional
(2019 International Conference on Machine Learning and Intelligent Systems (MLIS2019) 2019)
A convergence of the approximated free boundary of regularized functionals via Gamma-convergence
(The 2nd International Conference on Numerical Modelling in Engineering 2019)
Local existence for gradient flows via a minimizing scheme
(Free Boundary Problems and Nonlinear PDEs -- A symposium dedicated to prof. Seiro Omata on the occasion of his 60th birthday -- 2017)
