High frequency asymptotic analysis for nonlinear PDEs of hyperbolic and dispersive type
| Project/Area Number |
22740089
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Osaka University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2010 – 2012
|
| Project Status |
Completed (Fiscal Year 2012)
|
| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | 漸近解析 / 非線形波動 / シュレディンガー方程式 / 波動方程式 / クライン・ゴルドン方程式 |
|---|
| Research Abstract |
Nonlinear partial differential equations of hyperbolic and dispersive type are studied from the view point of high frequency asymptotic analysis. Relations between the null structure and resonant interactions are revealed for systems of nonlinear Klein-Gordon equations. Examples on small data blow-up for nonlinear Schrodinger equations are constructed, and estimates for the order of the lifespan of the blowing-up solutions are provided. The method of high frequency asymptotics are also applied to a class of nonlinear wave equations not satisfying the null condition.
|
Report
(4 results)
Research Products
(20 results)
