MIYAMOTO, Yasuhito

Nonlinear Partial Differential Equations
Research interests
Structure of nonlinear PDEs of elliptic and parabolic type
Current research

It is well known that nonlinear PDEs of elliptic and parabolic type can describe various phenomena arising in natural and social science. It is also known that there are many PDEs exhibiting interesting phenomena in a pure mathematical viewpoint. I am interested in the number of the solutions of those PDEs and properties of each solution including the shape and the Morse index.

Selected publications
  1. Y. Miyamoto, On connecting orbits of semilinear parabolic equations on S1, Documenta Mathematica, 9 (2004), 435--469.
  2. Y. Miyamoto, An instability criterion for activator-inhibitor systems in a two-dimensional ball II, Journal of Differential Equations, 239 (2007), 61--71.
  3. Y. Miyamoto, Global branches of non-radially symmetric solutions to a semilinear Neumann problem in a disk, Journal of Functional Analysis, 256 (2009), 747--776.
  4. Y. Miyamoto, The "hot spots" conjecture for a certain class of planar convex domains, Journal of Mathematical Physics, 50 (2009), 103530, 7 pp.
  5. Y. Miyamoto, A planar convex domain with many isolated "hot spots" on the boundary, Japan Journal of Indudstrial and Applied Mathematics, 30 (2013), 145-- 164.
  6. T. Kan and Y. Miyamoto, Analytic imperfect bifurcation theorem and the Liouville-Gel'fand equation on a perturbed annular domain, to appear in Mathematische Nachrichten.

Mathematical Society of Japan

Japan Society of Industrial and Applied Mathematics (JSIAM)


JSIAM Best Author Prize(2010)

MSJ Takebe Katahiro Prize(2010)

The Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology, The Young Scientists' Proze(2012)

Editorial Members of "Bulletin of the JSIAM"(2009--2011)