On a nonhomogeneous Burgers' equation
文献类型：期刊论文
| 作者 | Ding, XQ ; Jiu, QS; He, C
|
| 刊名 | SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY
 |
| 出版日期 | 2001-08-01 |
| 卷号 | 44期号:8页码:984-993 |
| 关键词 | nonhomogeneous Burgers' equation explicit solution large time behavior Hermite polynomials |
| ISSN号 | 1006-9283 |
| 英文摘要 | In this paper the Cauchy problem for the following nonhomogeneous Burgers' equation is considered: (1) u(t) + uu(x) = muu(xx) - kx, x is an element of R, t > 0, where mu and k are positive constants. Since the nonhomogeneous term kx does not belong to any LP( R) space, this type of equation is beyond usual Sobolev framework in some sense. By Hopf-Cole transformation, (1) takes the form (2) phi(t) = phi(xx) = -x(2)phi. With the help of the Hermite polynomials and their properties, (1) and (2) are solved exactly. Moreover, the large time behavior of the solutions is also considered, similar to the discussion in Hopf's paper. Especially, we observe that the nonhomogeneous Burgers' equation (1) is nonlinearly unstable. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000174374300005 |
| 出版者 | SCIENCE CHINA PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/16902]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Jiu, QS |
| 作者单位 | 1.Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Ding, XQ,Jiu, QS,He, C. On a nonhomogeneous Burgers' equation[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,2001,44(8):984-993. |
| APA | Ding, XQ,Jiu, QS,&He, C.(2001).On a nonhomogeneous Burgers' equation.SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY,44(8),984-993. |
| MLA | Ding, XQ,et al."On a nonhomogeneous Burgers' equation".SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY 44.8(2001):984-993. |
入库方式： OAI收割
来源：数学与系统科学研究院
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