KUBO, Hideo

KUBO, Hideo
Department of Mathematics
Research Interest
Theory of Partial Differential Equations
Research Activities

The wave equation is one of the typical partial differential equations and has a long history. Although the wave equation looks like so simple, its mathematical structure is quite rich. In my research the effect from some perturbation such as the nonlinear perturbation, the presence of an obstacle, and so on are analyzed. The main issue is to compare the leading term of a solution to the unperturbed system and that to the perturbed system. For instance, the scattering theory is nothing else but the comparison between the behavior of solutions to these systems as time goes to infinity. We use functional analysis and real analysis for studying the scattering theory. But heavy computations based on calculus are the core of our analysis. It is of special interest to consider the case where the effect from the perturbation is balanced with that from the unperturbed system, because such consideration enables us to see the essential feature of the unperturbed and perturbed systems. Recently, I’m also interested in systems appeared in mathematical physics which are reduced to the wave equation and in the non-commutative structure of some partial differential equations.

1. Hideo Kubo, Kôji Kubota, and Hideaki Sunagawa,
Large time behavior of solutions to semilinear systems of wave equations,
Math. Ann., 335 (2006), 435-478.

2. Hideo Kubo,
Asymptotic behavior of solutions to semilinear wave equations with dissipative structure,
Discrete and Continuous Dynamical Systems, Supplement 2007, 602-613.

3. Soichiro Katayama and Hideo Kubo,
An elementary proof of global existence for nonlinear wave equations in an exterior
domain, J. Math. Soc. Japan. 60 (2008), 1135-1170.

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