A study on the elliptic and the parabolic equations associated with noncompact variational structures
| Project/Area Number |
23540232
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Fukushima University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| Keywords | 非線型解析 / 変分法 / 楕円型方程式 / 放物型方程式 / エネルギー汎関数 / リャプノフ汎関数 / 非コンパクト性 / 変分問題 / コンパクト性の破れ / 臨界型関数不等式 / 国際情報交換 / 臨界問題 / 半線型放物型方程式 / 爆発解析 |
|---|
| Research Abstract |
In this research, we are concerned with the asymptotic behavior of time-global solutions for semilinear parabplic equations whose Lyapnov functional are suffered from the lack of compactness, togehter with the elliptic problem with variational functional with lack of compactness. Also we studeid the variational problem (minimizing problem) associated with the critical functional inequalities such as Sobolev, Hardy and the Trudinger-Moser type.
As for the parabolic problems, we treated the semilinear parabolic problem involving critical Sobolev exponent and showed the energy quantization phenomena for the time-global solutions. Also we studied the elliptic problem defined in the exterior domain with bounded complement with weight function decaying at the spatial infinity. We proved that if the decay of the weight function is sufiiciently slow, then the equations have multiple positive solutions.
|
Report
(4 results)
Research Products
(41 results)
