Multiplicity of solutions for the plasma problem in two dimensions
文献类型：期刊论文
| 作者 | Cao, Daomin1 ; Peng, Shuangjie2; Yan, Shusen3
|
| 刊名 | ADVANCES IN MATHEMATICS
 |
| 出版日期 | 2010-12-01 |
| 卷号 | 225期号:5页码:2741-2785 |
| 关键词 | Semilinear elliptic equations Variational method Multiple solutions Free boundary Asymptotic behavior |
| ISSN号 | 0001-8708 |
| DOI | 10.1016/j.aim.2010.05.012 |
| 英文摘要 | Let Omega be a bounded domain in R(2), u(+) = u if u >= 0, u(+) = 0 if u < 0, u(-) = u(+) - u. In this paper we study the existence of solutions to the following problem arising in the study of a simple model of a confined plasma (P(lambda)) {Delta u - lambda u(-) = o, in Omega, u = c, on partial derivative Omega, integral partial derivative u/partial derivative nu ds = I, partial derivative Omega where nu is the outward unit normal of partial derivative Omega at x, c is a constant which is unprescribed, and I is a given positive constant. The set Omega(p) = {x is an element of Omega, u(x) < 0} is called plasma set. Existence of solutions whose plasma set consisting of one component and asymptotic behavior of plasma set were studied by Caffarelli and Friedman (1980) [3] for large lambda. Under the condition that the homology of Omega is nontrivial we obtain in this paper by a constructive way that for any given integer k >= 1, there is lambda(k) > 0 such that for lambda > lambda(k), (P(lambda)) has a solution with plasma set consisting of k components. (C) 2010 Elsevier Inc. All rights reserved. |
| 资助项目 | Natural Science Foundation of China[10631030] ; Natural Science Foundation of China[10721101] ; Program for New Century Excellent Talents in University[07-0350] ; ARC in Australia |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000281888400017 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/9743]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Cao, Daomin |
| 作者单位 | 1.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China 2.Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China 3.Univ New England, Sch Math Stat & Comp Sci, Armidale, NSW 2351, Australia |
| 推荐引用方式 GB/T 7714 | Cao, Daomin,Peng, Shuangjie,Yan, Shusen. Multiplicity of solutions for the plasma problem in two dimensions[J]. ADVANCES IN MATHEMATICS,2010,225(5):2741-2785. |
| APA | Cao, Daomin,Peng, Shuangjie,&Yan, Shusen.(2010).Multiplicity of solutions for the plasma problem in two dimensions.ADVANCES IN MATHEMATICS,225(5),2741-2785. |
| MLA | Cao, Daomin,et al."Multiplicity of solutions for the plasma problem in two dimensions".ADVANCES IN MATHEMATICS 225.5(2010):2741-2785. |
入库方式： OAI收割
来源：数学与系统科学研究院
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