Stochastic analysis of fractal stochastic Burgers equation
| Project/Area Number |
25800060
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Shinshu University |
|---|
Principal Investigator |
XIE Bin 信州大学, 学術研究院理学系, 准教授 (50510038)
|
|---|
| Project Period (FY) |
2013-04-01 – 2016-03-31
|
| Project Status |
Completed (Fiscal Year 2015)
|
| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Keywords | 確率解析 / 確率偏微分方程式 / entropy solution / intermittency / 分数冪ラプラスアン / 確率エントロピー解 / 大偏差原理 / Intermittency / 確率熱方程式 / 分数階ラプラス作用素 / 確率バーガー型方程式 / Levy過程 |
|---|
| Outline of Final Research Achievements |
We mainly investigated the uniqueness and various properties to the solution of stochastic partial differential equations, by the approach of stochastic analysis. We first considered the uniqueness of stochastic fractal Burgers equations. By introducing a new kind of definition of solution, stochastic entropy solution, we proved the uniqueness of the solution in some proper state space. We also studied long time behavior relative to intermittency of stochastic reaction-diffusion equation driven by space-time white noise on a bounded domain, which are essentially depending on the estimate of its fundamental solution.
|
Report
(4 results)
Research Products
(11 results)
