Project/Area Number  09640186 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  KOBE UNIVERSITY 
Principal Investigator 
NAKAGIRI Shinichi Kobe University, Faculty of engineering Professor, 工学部, 教授 (20031148)

CoInvestigator(Kenkyūbuntansha) 
KAKIUCHI Itsurou Kobe University, Faculty of engineering Assoc.Professor, 工学部, 助教授 (90091248)
NAITO Yuki Kobe University, Faculty of engineering Assoc.Professor, 工学部, 助教授 (10231458)
TABATA Minoru Kobe University, Faculty of engineering Assoc.Professor, 工学部, 助教授 (70207215)
NAMBU Takao Kobe University, Faculty of engineering Professor, 工学部, 教授 (40156013)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥1,900,000 (Direct Cost : ¥1,900,000)
Fiscal Year 1998 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1997 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  optimal control / inverse problem / nonlinear distibuted systems / elliptic operator / identifiability / finite element method / semigroup / least square method / 最適制御 / 逆問題 / 非線形分布系 / 楕円型作用素 / 可同定性 / 有限要素法 / 半群理論 / 最少2乗法 / 最小2乗法 / 分数ベキ 
Research Abstract 
According to the research plan, we studied the existence and uniqueness of solutions for distributed parameter systems described by nonlinear second order evolution equations in the framework of variational method due to Lions. For the nonlinear systems we studied optimal control problems, and established necessary optimality conditions in terms of transposed systems for various types of observations. The conditions are new ones for nonlinear systems. The results were applied to practical systems such as sineGordon equation, KleinGordon equation, nonlinear damped beam equations and others. Next, for coupled sineGordon equations, we studied the numerical analysis of approximate solutions based on finite element method. As a result we observed the chaotic behavior of numerical solutions which depends heavily on physical parameters appearing in the equations. Further the head investigator studied the spatiallyvarying parameter identifiability in linear distributed parameter systems of parabolic and hyperbolic types by interior domain observations. This is a kind of inverse problems and he established several necessary and sufficient conditions for the identifiability. Also he solved the findpath problem of moving objects by means of Liapounof functions with the help of Drs. Ha and Vanualailai. The results of other investigatos are as follows. The investigator Nambu established the characterization of the domain of fractional powers of a class of elliptic differential operators with feedback boundary conditions. The investigator Tabata, by using the idea of optimality conditions, proposed and investigated the model equations for geographic spread of an epidemic. The investigator Naito studied nonlinear elliptic distributed parameter systems and established new conditions for the existence and nonexistence of positive radial solutions. The results of all investigators were published in the journals given below.
