非线性抛物椭圆方程组的正则解和奇异解

数学物理学报

非线性抛物椭圆方程组的正则解和奇异解

原保全

(河南理工大学数信学院河南焦作 454003); (中国科学院数学与系统科学研究院应用数学研究所北京 100190)

收稿日期:2006-04-05 修回日期:2007-12-01 出版日期:2008-08-25 发布日期:2008-08-25
通讯作者: 原保全
基金资助:
国家自然科学基金(10771052)、河南省自然科学基金(0611055500)、河南省教育厅自然科学基金(200510460008)、河南理工大学博士基金资助

Remark on the Regular and Singular Solutions to Nonlinear Parabolic-elliptic System

Yuan Baoquan

(Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Beijing 100080)

Received:2006-04-05 Revised:2007-12-01 Online:2008-08-25 Published:2008-08-25
Contact: Yuan Baoquan

摘要/Abstract

摘要： 该文用单模方法在Lorentz空间研究了抛物椭圆方程组奇异解和正则解的存在性, 其中初值属于Lorentz空间L^{n/2,∞ ₍}Rⁿ), n≥ 3. 利用时间加权的Lorentz空间, 还得到了其正则解. 此外, 如果初值满足自相似结构, 也得到了自相似解的存在性.

关键词: 抛物椭圆方程组, Lorentz 空间 Lⁿ^/2,∞ (Rⁿ), 奇异解和正则解

Abstract: This paper studies the existence of singular solutions to the nonlinear parabolic-elliptic system for initial data in Lorentz space Lⁿ^/2,∞ (Rⁿ), n≥3, only by means of the norm of Lorentz space. The regularized solutions are also obtained by virtue of the time weighted Lorentz space. Moreover, the self-similar solutions are also obtained.

Key words: Parabolic-elliptic system, Lorentz space Lⁿ^/2,∞ (Rⁿ), Regular and singular solutions

中图分类号:

35K40

原保全. 非线性抛物椭圆方程组的正则解和奇异解[J]. 数学物理学报, 2008, 28(4): 627-635.

Yuan Baoquan. Remark on the Regular and Singular Solutions to Nonlinear Parabolic-elliptic System[J]. Acta mathematica scientia,Series A, 2008, 28(4): 627-635.