2015 Fiscal Year Final Research Report
Generation, convergence and approximation of Lipschitz evolution operators in Banach spaces
Project/Area Number |
25400145
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
|
Research Institution | Chuo University |
Principal Investigator |
|
Co-Investigator(Kenkyū-buntansha) |
MATSUMOTO Toshitaka 静岡大学, 理学部, 教授 (20229561)
KOBAYASI Kazuo 早稲田大学, 教育・総合科学学術院, 教授 (80103612)
OHWA Hiroki 新潟大学, 自然科学系, 準教授 (10549158)
|
Project Period (FY) |
2013-04-01 – 2016-03-31
|
Keywords | 非線形発展方程式 / 非線形半群 / バナッハ空間 / 保存則系 / 非線形摂動 / 動力学的定式化 |
Outline of Final Research Achievements |
A new general class of Lipschitz evolution operators in Banach spaces is introduced and a characterization of the continuous infinitesimal generators of such evolution operators is obtained. It is given a necessary and sufficient condition for the existence of a weakly continuously differentiable solution to an abstract Cauchy problem in Banach spaces. Nonlinear perturbations of a holomorphic semigroup of fractional growth is studied through investigation of the associated Cauchy problems. Studying discontinuous mappings on intervals satisfying certain assumptions, it is shown that for such mappings there exist periodic points of period. In a kinetic formulation, it is obtained a result of uniqueness and existence of the initial-bounary value problem for a scalar first-order conservation law with a multicative noise.
|
Free Research Field |
発展方程式論
|