摘要
二阶线性抛物型方程混合问题的定解已臻完善,而半线性抛物型方程的混合问题多采用数值解法。本文则基于Stone-Weierstrass定理,以Riesz变分原理证明所述问题的可解性。同时,以圆域和材料各向同性的特性,依Sturm-Liouville问题,借助于Bessel函数系的正交性,用试探方法给出问题的迭代解列。再由Cauchy不等式证明算子的有累性,进而证明所求解列依范数收敛的性质。又根据正定算子的逆算子以及它与有界算子之积为全连续算子的结论而证明解列的极限函数即为本问题的解。
The definite solutions of mixed problem of the second order linear parabolic type equation have been solved perfectly, but most mixed problems of semi-linear parabolic type equation were solved only by the value solution method. In this paper, we will give the interative solution sequence of this problem here, the theories and methods, which we use, are as following, Stone-Weierstrass theory, solvability of this problem proven by Rieszs calculus of variatious, particularity of same direeted property of material, orthogonatily of Bessel's function system on Sturm-Liouville′s problem and explore method. At the same time, proven the boundness of operator by Cauchy′s mequality, futhermore, prove nthe convegence property of the solution sequance in the norm, then, according to converse operator of positive definite operator and the consequance that the production of bonded operator and converse operator of positive definite operator is complete conti nued operator, finally we will prove that the limit function of soluti on sequanee is the solution of this problem.
出处
《东北林业大学学报》
CAS
CSCD
北大核心
1989年第5期116-127,共12页
Journal of Northeast Forestry University
关键词
变分学
贝塞尔函数
选代法
收敛
Calculus of variations
Bessel
function
Iteration method
Convergence
Completely continuous operator
