研究者所属（当時）  資格  氏名  

（代表者）  理工学術院 先進理工学部  教授  大谷 光春 
（連携研究者）  応用物理学科  助教  内田 俊 
 研究成果概要

The following results are achieved under this grant.
(1) Study on the applications of “Linfinity Energy Method” to nonlinear partial differential equations:
We applied Linfinity Energy Method to the system of parabolic equations which describes a diffusionconvection preypredator model which takes into account of the hysteresis effects. Because of the strong nonlinearity of this system, we needed to improve some tools to establish a priori estimates for the Linfinity norm of solutions, by which we could ameliorate previous studies.
(2) Study on complex GinzburgLandau equations (CGLE):
(i) For the nondissipative system in bounded domains, we proved the existence and the uniqueness of timelocal solutions for CGLE in H^1space.
(ii) We analyzed the finitetime blowup of solutions of CGLE.
The previous studies dealt with the case where the energy of the initial data is negative in the whole domain.
We developed a new method to treat the case where the energy of the initial data is positive in general domains.
(3) Study on the mathematical analysis for the mitochondrial swelling model:
We analyzed this model with Robintype boundary conditions, which describes well the real situation of mitochondria in cells. We showed the well posedness of the system as well as the asymptotic behavior of solutions.