一类抛物方程的广义解

吴雨蒙

(吉林师范大学数学学院,吉林四平136000)

一类抛物方程的广义解

吴雨蒙

(吉林师范大学数学学院,吉林四平136000)

在自然科学的许多领域中，很多现象是用抛物方程描述的.因此,求解抛物偏微分方程问题具有重要的理论意义和应用价值.文章讨论了一类抛物方程非齐次边值问题的解法,先利用变量替换法,将这类抛物方程非齐次边值问题转化为齐次边值问题,然后再运用Lax-Milgram定理的推论证明了其解存在唯一性.

非齐次边值问题;能量方法;变量替换

[1]伍卓群,尹景学,王春朋.椭圆与抛物型方程引论[M].北京：科学出版社,2003.

[2]周蜀林.偏微分方程[M].北京：北京大学出版社,2005.

[3]亚当斯·索伯列夫空间[M].叶其孝,等译.北京：人民教育出版社,1981.

［责任编辑鲁海菊］

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

吴雨蒙(1991-),女,吉林扶余人,硕士生,研究方向：运筹学与控制论。