ISHIGE, Kazuhiro

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Title
Professor
Field
Partial Differential Equations
Research interests
Asymptotic analysis and geometric analysis for solutions to parabolic equations
Current research

I am interested in qualitative properties, in particular, the asymptotic behavior and geometric properties of solutions to parabolic equations. For example, I studied the movement of hot spots for parabolic equations; power concavity of solutions to parabolic equations; the solvability, the large time behavior and the blow-up phenomena for semilinear heat equations and systems, the heat equation with a nonlinear boundary condition and a semilinear elliptic equation with a dynamical boundary condition.
Selected publications
  1. K. Ishige and M. Murata, Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 30 (2001), 171--223.
  2. K. Ishige, Movement of hot spots on the exterior domain of a ball under the Neumann boundary condition, J. Differential Equations 212 ( 2005), 394--431.
  3. K. Ishige and Y. Kabeya, Lp norms of nonnegative Schrödinger heat semigroup and the large time behavior of hot spots, J. Funct. Anal. 262 (2012), 2695--2733.
  4. K. Ishige and T. Kawakami, Refined asymptotic profiles for a semilinear heat equation, Math. Ann. 353 (2012), 161-192.
  5. K. Ishige and P. Salani, Parabolic power concavity and parabolic boundary value problems, Math. Ann. 358 (2014), 1091-1117.
  6. Y. Fujishima and K. Ishige, Blow-up set for type I blowing up solutions for a semilinear heat equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), 231--247.
  7. N. Ioku, K. Ishige and E. Yanagida, Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups, J. Math. Pures Appl. 103 (2015), 900-923.
  8. K. Ishige and P. Salani, Parabolic Minkowski convolution of solutions for parabolic boundary value problems, Adv. Math. 287 (2016), 640-673.
  9. M. Fila, K. Ishige and T. Kawakami, Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition, J. Math. Pures Appl. 105 (2016), 788--809.
  10. Y. Fujishima, K. Ishige and H. Maekawa, Blow-up set of type I blowing up solutions for nonlinear parabolic systems, Math. Ann. 369 ( 2017), 1491--1525.
Books
 F. Gazzola, K. Ishige, C. Nitsch and P. Salani, Geometric Propertties for Parabolic and Elliptic PDE's, Springer Proceedings in Mathematics & Statistics, Vol. 176, Springer International Publishing Switzerland (2016).
Memberships

The Mathematical Society of Japan
The Japan Society for Industrial and Applied Mathematics
Awards
 Seiichi Tejima Doctoral Dissertation Award, 1996
Division of Functional Equations, The Mathematical Society of Japan, The Hukuhara Prize, 2009
The Mathematical Society of Japan, The MSJ Analysis Prize, 2014