KURODA, Hirotoshi
 Position
 Associate Professor
 Organization
 Department of Mathematics
 Research Interest
 Partial Differential equations
 Research Activities

I am interested in partial differential equations which are relation to variational problems. So I especially study the gradient flow of the total variation that describes a process to remove a noise from the original image in the image processing. Since the total variation flow has a strong singularity, the subdifferential for convex functions and the nonlinear semigroup theory are useful to analyze its solvability and asymptotic behavior. These days I have an interest in the thin domain problems.
Papers:
1.Y. Giga and H. Kuroda, A counterexample to finite time stopping property for oneharmonic map flow, Commun. Pure Appl. Anal., 14(2015), no.1, 121125.
2.Y. Giga, H. Kuroda and H. Matsuoka, Fourthorder total variation flow with Dirichlet condition: Characterization of evolution and extinction time estimates, Adv. Math. Sci. Appl., 24(2014), no.2, 499534.
3.H. Kuroda and N. Yamazaki, Approximating problems of vectorial singular diffusion equations with inhomogeneous terms and numerical simulations, Discrete Contin. Dyn. Syst. 2009, Dynamical Systems, Differential Equations and Applications. 7th AIMS Conference, Suppl., (2009), 486495.  Keywords
 Mosco convergence, nonlinear semigroup theory, total variation, variational problem
 WebPage
 http://www7b.biglobe.ne.jp/~hkuroda/