Stability of planar diffusion wave for nonlinear evolution equation
文献类型：期刊论文
| 作者 | He Cheng1; Huang FeiMin3 ; Yong Yan2
|
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2012 |
| 卷号 | 55期号:2页码:337-352 |
| 关键词 | HYPERBOLIC CONSERVATION-LAWS THROUGH POROUS-MEDIA P-SYSTEM ASYMPTOTIC-BEHAVIOR CONVERGENCE FLOW MULTIDIMENSIONS RATES stability planar diffusion wave nonlinear evolution equation |
| ISSN号 | 1674-7283 |
| 其他题名 | Stability of planar diffusion wave for nonlinear evolution equation |
| 英文摘要 | It is known that the one-dimensional nonlinear heat equation u(t) = f(u)(x1 x1), f' (u) > 0, u(+/-infinity, t) = u(+/-), u(+) not equal u(-) has a unique self-similar solution (u) over bar( x(1)/root 1+t). In multi-dimensional space, (u) over bar( x(1)/root 1+t) is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation: u(t) - Delta f(u) = 0, x is an element of R-n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with clamping: u(tt) + u(t) - Delta f(u) = 0, x is an element of R-n. The time decay rate is also obtained. The proofs are given by an elementary energy method. |
| 资助项目 | [National Basic Research Program of China] ; [National Natural Science Foundation of China for Distinguished Youth Scholar] ; [NSFC-NSAF] |
| 语种 | 英语 |
| CSCD记录号 | CSCD:4537845 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/56365]  |
| 专题 | 应用数学研究所 |
| 作者单位 | 1.Natl Nat Science Fdn China, Beijing I00085, Peoples R China 2.上海大学 3.中国科学院数学与系统科学研究院 |
| 推荐引用方式 GB/T 7714 | He Cheng,Huang FeiMin,Yong Yan. Stability of planar diffusion wave for nonlinear evolution equation[J]. SCIENCE CHINA-MATHEMATICS,2012,55(2):337-352. |
| APA | He Cheng,Huang FeiMin,&Yong Yan.(2012).Stability of planar diffusion wave for nonlinear evolution equation.SCIENCE CHINA-MATHEMATICS,55(2),337-352. |
| MLA | He Cheng,et al."Stability of planar diffusion wave for nonlinear evolution equation".SCIENCE CHINA-MATHEMATICS 55.2(2012):337-352. |
入库方式： OAI收割
来源：数学与系统科学研究院
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