| 摘要: |
| 基于椭圆算子,证明初边值问题:∂u/∂t-λ(∂/∂t)(∂2u/∂x2)+(∂4Φ(u))/∂x4=0,(x,t)∈QT,u(0,t)=u(1,t)=ux(0,t)=ux(1,t)=0,t∈(0,T),u(x,0)=u0(x),x∈(0,1),λ ≥ 0是粘性系数,QT=(0,1)×(0,T),Φ(u)=|u|q-2u,q>1,最多存在一个L2解。 |
| 关键词: 扩散方程 粘性 解 唯一性 椭圆算子 |
| DOI： |
| 投稿时间：2006-12-25修订日期：2007-03-12 |
| 基金项目:2006年广西教育厅科研项目(编号:234)资助 |
|
| Uniqueness of Solutions to a Fourth Order Viscous Diffusion Equation |
|
QIN Si-qian, LING Zheng-qiu
|
| (Department of Mathematics and Computation Science, Yulin Teachers'College, Yulin, Guangxi, 537000, China) |
| Abstract: |
| Based on elliptic operators,the initial boundary value problem:∂u/∂t-λ(∂/∂t)(∂2u/∂x2)+(∂4Φ(u))/∂x4=0,(x,t)∈QT,u(0,t)=u(1,t)=ux(0,t)=ux(1,t)=0,t∈(0,T),u(x,0)=u0(x),x∈(0,1),λ ≥ 0,QT=(0,1)×(o,T),Φ(u)=|u|q-2u,q>1,has at most one L2 solution. |
| Key words: diffusion equation viscous solution uniqueness elliptic operator |
