1988 Fiscal Year Final Research Report Summary
The comprehensive study of differential equations
| Project/Area Number |
62302004
|
|---|
| Research Category |
Grant-in-Aid for Co-operative Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
解析学
|
|---|
| Research Institution | HIROSHIMA UNIVERSITY |
|---|
Principal Investigator |
KUSANO Takasi Faculty of Science, Hiroshima University; Professor, 理学部, 教授 (70033868)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
AIZAWA Sadakazu Faculty of Science, Kobe University; Professor, 理学部, 教授 (20030760)
MOCHIZUKI Kiyoshi Faculty of Science, Shinshu University; Professor, 理学部, 教授 (80026773)
KIMURA Tosihusa Faculty of Science, University of Tokyo; Professor, 理学部, 教授 (50011466)
SHIMAKURA Norio Faculty of Science, Tohoku University; Professor, 理学部, 教授 (60025393)
AGEMI Rentaro Faculty of Science, Hokkaido University; Professor, 理学部, 教授 (10000845)
|
|---|
| Project Period (FY) |
1987 – 1988
|
| Keywords | Ordinary differential equation / Partial differential equation / Functional differential equation / Linear / Nonlinear / Solution / Existence / Uniqueness / Asymptotic behavior |
|---|
| Research Abstract |
The present research project covers both ordinary differential equations and partial differential equations. As a consequence of active, enthusiastic and energetic investigations by the members of the group of researchers, organized for this project, a great number of significant and important results have been obtained in various branches of differential equations as listed below:
(1) qualitative theory of nonlinear ordinary differential equations in the real domain;
(2) analytic theory of ordinary and partial differential equations in the complex domain;
(3) fundamential existence-uniqueness theory for linear partial differential equations of hyperbolic, elliptic and parabolic types;
(4) theory of pseudo-differential operators;
(5) scattering theory for wave and elastic wave equations;
(6) the problem of existence and qualitative behavior of positive solutions of nonlinear elliptic partial differential equations in unbounded domains;
(7) global existence and asymptotic behavior of solutions for nonlinear partial differential equations (or systems) of parabolic and hyperbolic types;
(8) various fundamental problems for nonlinear partial differential equations arising in fulid dynamics and other applied sciences, such as the Navier-Stokes equation and the Boltzmann equation.
Praticular mention is made of the new results obtained by the head investigator regarding
(i) oscillation theory of higher order functional differential equations of neutral type;
(ii) existence of various types of positive entire solutions for second order quasilinear elliptic equations generalizing the equation of prescribed mean curvature; and
(iii) classification of positive entire solutions of a class of semilinear elliptic equations of arbitrary order.
|
