一類拋物方程的廣義解

吳雨蒙

(吉林師范大學數學學院,吉林四平136000)

一類拋物方程的廣義解

吳雨蒙

(吉林師范大學數學學院,吉林四平136000)

在自然科學的許多領域中，很多現象是用拋物方程描述的.因此,求解拋物偏微分方程問題具有重要的理論意義和應用價值.文章討論了一類拋物方程非齊次邊值問題的解法,先利用變量替換法,將這類拋物方程非齊次邊值問題轉化為齊次邊值問題,然后再運用Lax-Milgram定理的推論證明了其解存在唯一性.

非齊次邊值問題;能量方法;變量替換

[1]伍卓群,尹景學,王春朋.橢圓與拋物型方程引論[M].北京：科學出版社,2003.

[2]周蜀林.偏微分方程[M].北京：北京大學出版社,2005.

[3]亞當斯·索伯列夫空間[M].葉其孝,等譯.北京：人民教育出版社,1981.

［責任編輯魯海菊］

The Generalized Solutions of a Class of Parabolic Equations

WU Yu-meng
(College of Mathematics,Jilin Normal University,Siping 136000,China)

In many fields of natural science,a lot of parabolic equation is used to describe the phenomenon,therefore,solving parabolic partial differential equation problems has important theoretical significance and application value.This paper discusses a class of Parabolic Equations with non-homogeneous boundary value problem solution,using the method of variable replacement to transform the non-homogeneous boundary value problem into a homogeneous boundary value problem,and using the Lax-Milgram theorem proving the existence and uniqueness of the solution.

Non-homogeneous boundary value problem；Energy method；Variable substitution

O175.26

A

1008-9128(2015)05-0023-04

2014-09-09

吳雨蒙(1991-),女,吉林扶余人,碩士生,研究方向：運籌學與控制論。