Cooperative Faculty Member

KURODA, Hirotoshi

Position
Specially Appointed Associate Professor
Organization
Program for Leading Graduate Schools Promotion Office, Faculty of Science
Research Field
Partial Differential equations
Keywords
variational problem, total variation, nonlinear semigroup theory, Mosco convergence
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 one-harmonic map flow, Commun. Pure Appl. Anal., 14(2015), no.1, 121-125.
2.Y. Giga, H. Kuroda and H. Matsuoka, Fourth-order total variation flow with Dirichlet condition: Characterization of evolution and extinction time estimates, Adv. Math. Sci. Appl., 24(2014), no.2, 499-534.
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), 486-495.
Personal webpage
http://www7b.biglobe.ne.jp/~h-kuroda/

YOSHIYASU, Toru

Position
Professional staff
Organization
Institute for the Advancement of Higher Education
Research Field
Symplectic Geometry
Keywords
h-principle, Lagrangian submanifold
Research Activities
I am interested in flexibilities in Symplectic Geometry. I study the topology of Lagrangian submanifolds by using the theory of h-principles. These days, I also have an interest in flexibility phenomena of limits in Symplectic Geometry.
Papers:
1. T. Yoshiyasu, On Lagrangian embeddings into the complex projective spaces, Internat. J. Math. 27 (2016), no. 5, 1650044, 12 pp.
2. N. Kasuya and T. Yoshiyasu, On Lagrangian embeddings of parallelizable manifolds, Internat. J. Math. 24 (2013), no. 9, 1350073, 9 pp.
Personal webpage
https://sites.google.com/site/toruyoshiyasu/

YORDANOV, Borislav

Position
Assistant Professor
Organization
Office of International Affairs
Research Field
Hyperbolic Partial Differential Equations
Keywords
Nonlinear wave equation, Diffusion Phenomenon, Nonlinear Damping
Research Activities
My research interests lie in the field of dissipative linear and nonlinear hyperbolic PDEs. The study of such equations has been inspired by theoretical physics. Indeed, hyperbolic equations arise in some of the fundamental theories including general relativity, quantum field theory, electrodynamics, acoustics and elasticity.
My recent work concerns two problems: (1) global well-posedness for nonlinear wave equations with critical and supercritical damping and (2) asymptotic behavior for dissipative wave equations related to the so-called diffusion approximation of damped waves.
Papers:
1. P. Radu, G. Todorova and B. Yordanov, The Generalized Diffusion Phenomenon and Applications, accepted in SIAM Journal of Math. Anal., 2015.
 
2. G. Todorova and B. Yordanov, On the Regularizing Effect of Nonlinear Damping in Hyperbolic Equations, Trans. Amer. Math. Soc., 367 (2015), 5043-5058.
 
3. R. Ikehata, G. Todorova and B. Yordanov, Diffusion Phenomenon for Strongly Damped Wave Equations, J. Diff. Equations 254 (2013), 3352-3368.