2006 Fiscal Year Final Research Report Summary
Inverse problems in Mathematical Biology, Chemistry and Technology
| Project/Area Number |
16340031
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | University of Tsukuba |
|---|
Principal Investigator |
TAIRA Kazuaki University of Tsukuba, Graduate School of Pure and Applied Sciences, Professor, 大学院数理物質科学研究科, 教授 (90016163)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
WAKABAYASHI Seiichiro University of Tsukuba, Graduate School of Pure and Applied Sciences, Professor, 大学院数理物質科学研究科, 教授 (10015894)
KINOSHITA Tamotu University of Tsukuba, Graduate School of Pure and Applied Sciences, Instrucror, 大学院数理物質科学研究科, 講師 (90301077)
MIYACHI Akihiko Tokyo Women's Christian University, Department of Mathematics, Professor, 文理学部, 教授 (60107696)
YAGI Atsushi Osaka University, Faculty of Technology, Professor, 大学院工学研究科, 教授 (70116119)
UMEZU Kenichiro Maebashi Institute of Technology, Faculty of Technology, Associate Professor, 工学部, 助教授 (00295453)
|
|---|
| Project Period (FY) |
2004 – 2006
|
| Keywords | Mathematical Biology / Technology / Inverse Problem / Nonlinear Boundary Value Problem / Singular Integral / Diffusion Process / Variational Method |
|---|
| Research Abstract |
Our results may be summarized as follows:
1. First, we studied the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Second-order elliptic differential operators with discontinuous coefficients enter naturally in connection with the problem of construction of Markov processes in probability. Our approach here is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of Calderon and Zygmund of singular integral operators with non-smooth kernels. The presentation of these new results is the main purpose of our research.
2. Secondly, we studied existence and uniqueness problems of positive solutions of diffusive logistic equations with indefinite weights which model population dynamics in environments with strong spatial heterogeneity. We discussed the changes that occur in the structure of the positive solutions as a parameter varies near the first eigenvalue of the linearized problem, and proved that the most favorable situations will occur if there is a relatively large favorable region (with good resources and without crowding effects) located some distance away from the boundary of the environment.
|
