一類非線性拋物方程Cauchy問題解的存在性條件

陳美珍,潘佳慶

(集美大學理學院,福建廈門 361021)

一類非線性拋物方程Cauchy問題解的存在性條件

陳美珍,潘佳慶

(集美大學理學院,福建廈門 361021)

研究了帶源項的非線性拋物方程Cauchy問題解存在的必要條件以及解所應具有的性質,通過把文獻中的線性算子推廣到形式較一般的帶源項的非線性拋物算子,利用其中處理線性問題的方法來處理非線性問題.

Cauchy問題;必要條件;L1可積

1 引言

2 定理及其證明

參考文獻

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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.

陳美珍(1986-),碩士生.研究方向:非線性數學物理.

潘佳慶(1957-),博士,教授.研究方向:偏微分方程,流體力學.

2010 MSC:35K10,35K15,35K55