一类抛物方程的广义解

The Generalized Solutions of a Class of Parabolic Equations

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.

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