# Hiroyuki Takamura

Department | Department of Complex and Intelligent Systems |
---|---|

Specialized Fields | Nonlinear Partial Differential Equations |

Subjects in Charge | |

Academic Background | Master course in Department of Mathematics, Hokkaido University |

Degree | Ph.D. in Science, Hoakkaido University (no.4781), June 1995. |

Personal History | Assistant in Department of Mathematics, University of Tsukuba, April 1992-May 1997. Lecturer in Department of Mathematics, University of Tsukuba, June 1997-August 2003 Associate professor in Future University Haokodate, Septmber 2003-March 2012. Professor in Future University, April 2012-" |

Starting Time of Employment | 1-Sep-03 |

## Research Contents

Partial Differential Equations, Nonlinear Wave Eqautions. (Pure Math.)

## Attractive Factors of My Research

I always have a possibility to be a pioneer in the world.

## Achievements

In 2011, I have succeeded to solve the final problem on the optimailty of the general theory for nonlinear wave equations. I have spent almost 20 years with this problem which has been very famous in this field. The result is already published as [10] below. Due to this work, I have received “the 5th Hukuhara prize” from the Mathematical Society of Japan for my contribution to the development of “The Division of Functional Equations” with my research on “Blow-up of solutions to semilinear wave equations”. Please take a look

http://mathsoc.jp/section/dfe/index-e.html

## Major Books and Papers

1. N.-A.Lai & H.Takamura, "Blow-up for semilinear wave equations with sub-Strauss exponent in the scattering case", submitted (arXiv:1707.09583).

2. N.-A.Lai & H.Takamura & K.Wakasa, "Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent", J.Differential Equations, in press (arXiv:1701.03232).

3. T.Imai & M.Kato & H.Takamura & K. Wakasa, "The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions", Proceeding of the international conference "Asymptotic Analysis for Nonlinear Dispersive and Wave Equations" of a volume in Advanced Study of Pure Mathematics, to appear (arXiv.1610.05913).

4. H.Takamura & K.Wakasa, "Global existence for semilinear wave equations with the critical blow-up term in high dimensions", J.Differential Equations, 261(2) (2016), 1046-1067.

5. M.A.Rammaha & H.Takamura & H.Uesaka & K.Wakasa, "Blow-up of positive solutions to wave equations in high dimensions", Differential and integral equations, 29 (1-2) (2016), 1-18.

6. H.Takamura, "Improved Kato's lemma on ordinary differential inequality and its application to semilinear wave equations", Nonlinear Analysis TMA, 125 (2015), 227-240.

7. H.Takamura & K.Wakasa, "Almost global solutions of semilinear wave equations with the critical exponent in high dimensions", Nonlinear Analysis, TMA 109 (2014), 187-229.

8. Y.Kurokawa & H.Takamura & K.Wakasa, "The blow-up and lifespan of solutions to systems of semilinear wave equation with critical exponents in high dimensions", Differential and Integral Equations 25(3-4)(2012), pp.363-382.

9. H.Takamura & K.Wakasa, "The final problem on the optimality of the general theory for nonlinear wave equations", Progress in Mathematics vol.301, M.Ruzhansky & M.Sugimoto & J.Wirth (eds.), "Evolution Equations of Hyperbolic and Schr"odinger Type", (2012), pp.315-324.

10. H.Takamura & K.Wakasa, "The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions", J.Differential Equations, 251(4-5) (2011), pp.1157-1171.

11. H.Takamura & H.Uesaka & K.Wakasa, "Sharp blow-up for semilinear wave eqautions with non-compactly supported data", Discrete and Continuous Dynamical Systems, Supplement (2011), pp.1351-1357.

12. H.Takamura & H.Uesaka & K.Wakasa, "Blow-up theorem for semilinear wave equations with non-zero initial position", J.Differential Equations, 249(4)(2010), pp.914-930.

## Message to Students

Please take a look for my data in MathSciNet. If you have any question, please contact me by e-mail at the address in my recent paper.