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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 blowup 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

 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), 171223.
 K. Ishige, Movement of hot spots on the exterior domain of a ball
under the Neumann boundary condition, J. Differential Equations 212 (
2005), 394431.
 K. Ishige and Y. Kabeya, L^{p} norms of nonnegative Schrödinger heat
semigroup and the large time behavior of hot spots, J. Funct. Anal. 262
(2012), 26952733.
 K. Ishige and T. Kawakami, Refined asymptotic profiles for a
semilinear heat equation,
Math. Ann. 353 (2012), 161192.
 K. Ishige and P. Salani, Parabolic power concavity and parabolic
boundary value problems, Math. Ann. 358 (2014), 10911117.
 Y. Fujishima and K. Ishige, Blowup set for type I blowing up
solutions for a semilinear heat equation, Ann. Inst. H. Poincaré Anal.
Non Linéaire 31 (2014), 231247.
 N. Ioku, K. Ishige and E. Yanagida, Sharp decay estimates in Lorentz
spaces for nonnegative Schrödinger heat semigroups, J. Math. Pures
Appl. 103 (2015), 900923.
 K. Ishige and P. Salani, Parabolic Minkowski convolution of solutions
for parabolic boundary value problems, Adv. Math. 287 (2016), 640673.
 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), 788809.
 Y. Fujishima, K. Ishige and H. Maekawa, Blowup set of type I
blowing up solutions for nonlinear parabolic systems, Math. Ann. 369 (
2017), 14911525.

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 