一类重特征双曲算子的Cauchy问题的拟基本解

一类重特征双曲算子的Cauchy问题的拟基本解 ON THE PARAMETRIX OF CAUCHY PROBLEM FOR A CLASS OF HYPERBOLIC OPERATORS WITH MULTIPLE CHARACTERISTICS 吴方同 Wu Fangtong first-author 本文讨论了一类具有重特征的二阶双曲算子组的Cauchy问题,采用渐近方法和付立叶积分算子为工具构造了拟基本解. Let M be an n+1-dimensional smooth manifold, locally M={（x 0 , x 1 , …, x n ）}. M 0 ={x 0 =0}（?）M, dim M 0 =n. We note that（x 0 , x 1 , …, x n ）=（x 0 , x）. We consider the operator L=D x 0 +（Tl（（?）, D x ） l（（?）, D x ））+B（x 0 , x, D x ） where l（x, ξ）is real value and homogeneous of degreelin ξ, and l（x, ξ）∈S 1 （M 0 ×R n ）, B（x 0 , x, ξ）∈S 0 （M×R n ）, T is the constant. The restriction operator ρ 0 : C ∞ （M）→C ∞ （M 0 ） is a Fourier integral operator of class I 1/4 （M 0 , M, R 0 ）, defined by the homogeneous canonical relation R 0 ={（（x, ξ）, （0, x, ξ 0 , ξ））∈T * M 0 ×T * M\0} We construct the pramtrix E of cauchy problem for L, wich satisfies where I is identity operator on ε ′ （M 0 ）. We obtained that E=E 1 +E 2 +E 3 , where E 1 is a psudo-differential operator, E 2 is a Fourier integral operator, E 3 is a slightly more complicated operator. 余法丛 齐次典则关系 辛正交 李导数 Maslov线丛 波前集拟基本解 付立叶积分算子 中国科学院科学基金 1987-02-01 2021-04-01 2