一类非线性抛物方程Cauchy问题解的存在性条件

陈美珍,潘佳庆

(集美大学理学院,福建厦门 361021)

一类非线性抛物方程Cauchy问题解的存在性条件

陈美珍,潘佳庆

(集美大学理学院,福建厦门 361021)

研究了带源项的非线性抛物方程Cauchy问题解存在的必要条件以及解所应具有的性质,通过把文献中的线性算子推广到形式较一般的带源项的非线性抛物算子,利用其中处理线性问题的方法来处理非线性问题.

Cauchy问题;必要条件;L1可积

1 引言

2 定理及其证明

参考文献

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The existence conditions of solutions of a class of nonlinear parabolic equation

Chen Meizhen,Pan Jiaqing

(School of Science,Jimei University,Xiamen361021,China)

This paper discusses the necessary conditions of solution to a class of nonlinear parabolic equation and the nature of the solution.By extending the linear operator to a more general form of nonlinear parabolic operator with the source term,we use the method in document which was used to handle the linear problem to handle the nonlinear problem.

the Cauchy problem,the necessary conditions,L1integrable

O175.26

A

1008-5513(2013)06-0654-07

10.3969/j.issn.1008-5513.2013.06.016

2013-11-01.

陈美珍(1986-),硕士生.研究方向:非线性数学物理.

潘佳庆(1957-),博士,教授.研究方向:偏微分方程,流体力学.

2010 MSC:35K10,35K15,35K55