Professor Tatsuya Watanabe
|Area and Subject Taught||Functional Analysis|
|Research Theme(s)||Research on elliptic PDEs by the variational method|
|Academic Degrees||Doctor (Mathematics), Tokyo Metropolitan University|
|Keywords for Research Field||Variational method, Elliptic PDE|
|Office Phone Number||81-75-705-1616|
Many differential equations which describe various natural phenomena have the variational structure and solutions can be obtained as critical points of the energy functional. When we study the dynamics of the solutions, it is important to know their characterizations and asymptotic behaviors. My research theme is to study the existence, characterizations, shapes and asymptotic behaviors of solutions of various differential equations which have the variational structure by analyzing the energy functional. Especially I’m interested in how physical parameters contained in differential equations can affect the solution set.
Among various differential equations, I’m mainly studying nonlinear elliptic partial differential equations which appear as stationary problems of nonlinear Schrödinger equations. Moreover, based on the analysis of the solution sets for stationary problems, I investigate the stability of standing waves for the corresponding evolution problems. I’m also studying mathematical models which describe the deformation of elastic membranes, eigenvalue optimization problems, asymptotic behavior of global solutions for parabolic PDEs and periodic solutions of hyperbolic PDEs.
Notable Publications and Works in the Last Three Years
- Pablo Alvarez-Caudevilla and Tatsuya Watanabe, On the existence of coexistence states for an Advection-Cooperative system with spatial heterogeneities, Nonlinear Analysis, 152 (2017), 12--37.
- Shinji Adachi, Masataka Shibata and Tatsuya Watanabe, Global uniqueness results for ground states for a class of quasilinear elliptic equations, Kodai Mathematical Journal, 40 (2017), 117--142.
- Mathieu Colin and Tatsuya Watanabe, Cauchy problem for the nonlinear Klein-Gordon equation coupled with the Maxwell equation, Journal of Mathematical Analysis and Applications, 443 (2016), 778--796.
- Shinji Adachi and Tatsuya Watanabe, Asymptotic uniqueness of ground states for a class of quasilinear Schrödinger equations with H^1-supercritical exponent, Journal of Differential Equations, 260 (2016), 3086--3118.