两个自变数三个未知函数的二阶常系数线性双曲型、复合型、抛物型偏微分方程组的通解 |
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引用本文: | 林海明.两个自变数三个未知函数的二阶常系数线性双曲型、复合型、抛物型偏微分方程组的通解[J].贵州师范大学学报(自然科学版),1988(1). |
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作者姓名: | 林海明 |
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作者单位: | 贵州师大数学系 |
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摘 要: | 在这篇文章中,我们考虑了问题:求函数u=(u_1,U_2,u_3)~T满足方程:A ( ~2u/ x~2)+2B( ~2u/ x y)+C( ~2u/ y~2)(Ⅰ)这里A、B、C为3阶常数矩阵。得到了方程(Ⅰ)的一个可分解等价条件;在标准形方面,我们指出了方程(Ⅰ)与〔1〕中方程的不同之处;给出了方程(Ⅰ)在等价变换下双曲型、复合型、抛物型方程的通解。
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CONSTANT COEFFIECINT LINEAR HYPERBOLIC MIXED AND PARABOLIC TYPE PARTIAL DIFFERENTIAL EQUATION SYSTEM OF SECOND OD RERWIH TWO VARIABLES THREE UNKNOW FOUNCTIONS |
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Abstract: | In this paper we consider the problem:Find fonction u=(u_1u_2u_3) satisty equation A ( ~2u/ x~2)+2B( ~2u/ x y)+C( ~2u/ y~2) here A,B,C are given 3 orders constant matrix We obtain a equivalent condition that eqation (Ⅰ) is disovable point out some different between equation(Ⅰ)and〔1〕,sequation in stan dard form, give all solution of hyperbolic,mixed and parabolic type equationsystem (Ⅰ) under equivalent transformation. |
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