KITA Kosuke Assistant Professor
Research Activities
My research interests can be divided into two main areas. One is reaction-diffusion equations with nonlinear boundary conditions as in thermal radiation, and the other is the telegraph equation (damped wave equation), which describes wave propagation phenomena with energy dissipation, or its nonlinear problem. Since it is difficult to controll the heat flux on the boundary of the domain for a large system such as a nuclear reactor, a nonlinear boundary condition that takes into account thermal radiation, as in Stefan–Boltzmann’s law, is a natural choice. We are studying the qualitative theory of solutions for reaction-diffusion equations with nonlinear boundary conditions. My other interest is a pointwise estimate for the solution of the damped wave equation. The damped wave equation is known to have the properties of both the heat (diffusion) equation, which is a typical example of a parabolic equation, and the wave equation, which is a typical example of a hyperbolic equation.
Papers
- V. Georgiev and K. Kita, Weighted $L^\infty$-estimates for solutions of the damped wave equation in three space dimensions and its application, submitted.
- K. Kita, K. Matsushima and T. Oka, Optimal design problem with thermal radiation, submitted. (arXiv:2408.00021)
- K. Kita and R. Kusaba, A remark on the blowing up of solutions to Nakao’s problem, Journal of Mathematical Analysis and Applications, 513(2022), No. 1, 126199.
- K. Kita and M. Ôtani, On a comparison theorem for parabolic equations with nonlinear boundary conditions, Advances in Nonlinear Analysis, 11(2022), No. 1, 1165-1181.
WebPage
Contact
kosuke.kita（at）math.sci.hokudai.ac.jp