ON CHANGING THE VARIABLE IN DISTRIBUTIONS

This paper proves the existence of the distributions (x_ ~r)_ ~(-8), (x_ ~r)_-~(-8), (x_-~(-8))_ ~(-8), (-x_ ~r)_-~(-8), (-x_-~r)_-~(-8), (x_ ~r)~(-s), |X_ ~r|~(-s) and sgn X·|X_ ~r|~(-s) and shows their corresponding expressions by means of the changes of independent variable and the neutrix limits in distributions.     

赫姆霍兹方程在聚焦面旁的渐近解

本文用短波近似法求得赫姆霍兹方程(3)在光滑凸聚焦面近旁的渐近解,并讨论了有关问题的物理意义.     

ASYMPTOTIC SOLUTIONS OF THE REDUCED WAVE EQUATION IN THE VICINITY OF A HIGHER CAUSTIC

In this paper the asymptotic solutions of the reduced wave equation (1) in the vicinity of a higher caustic have been found out by means of asymptotic expansions of the generalized Airy function, and the order (or the singularity inder) and the phase's increment of solutions on the higher caustic have been obtained, too.     

UNIFORM ASYMPTOTIC EXPANSIONS OF SOLUTION FOR THE REDUCED WAVE EQUATION AT A CUSPED CAUSTIC

The uniform asymptotic expansions of solution for reduced wave equation (1) at a cusped caustic are considered in the paper, the asymptotic solution (2) on the cusped caustic is obtained by means of the method of steepest descent, which shows that the singularity of solution is enhanced by order 1/6 on the caustic.     

高阶稳定位相定理

本文应用广义Airy函数的渐近展开式求得含大参数k的积分(1)的高阶稳定位相定理。     

KdV-Burgers方程的Cauchy问题

本文用摄动法求得KdV-Burgers方程初值问题的渐近解,并在L_2和L_∞范数的意义下讨论了解的唯一性和稳定性。     

高维广义BBM方程组的初边值问题

本文应用先验估计和Galerkin方法证明了高维广义BBM方程组的初边值问题在L~∞(0,T;H~3(Ω)∩H_0~1(Ω)),(s≥2)中整体解的存在性和正则性,并得到了整体解在||·||_(H~3×L~∞)范数下的稳定性和光滑解的唯一性。     

赫姆霍兹方程在聚焦面旁的渐近解

本文用短波近似法求得赫姆霍兹方程(3)在光滑凸聚焦面近旁的渐近解,并讨论了有关问题的物理意义。