这两个偏微分方程都是非线性调和方程。
These partial differential equations are all nonlinear harmonic equations.
调和方程的解与微分形式之间有着密切的联系。
The solution of A-harmonic equation and the differential forms have many affinities.
本文以调和方程为例，研究椭圆外区域上的自然边界无法。
In this paper we discuss the natural boundary element method for harmonic equation in an exterior elliptic domain.
研究了椭圆外无穷扇形区域上调和方程边值问题的自然边界元法。
In this paper, we investigate the natural boundary element method for the boundary value problem of harmonic equation in an exterior elliptic infinite sector domain.
讨论了带非负扰动的临界非齐次多重调和方程多解存在性和非存在性。
This paper deals with the existence and nonexistence of solutions for a critical semilinear polyharmonic equation with a non-negative perturbation.
利用Green函数，根据双调和方程边值问题的边界积分公式和自然边界积分方程。
By using Green function, the boundary integral formula and natural boundary integral equation for the boundary value problems of biharmonic equation were obtained.
讨论了带非负扰动并具有第二类边值的临界非齐次多重调和方程的多解存在性和非存在性。
This paper deals with the existence and nonexistence of solutions for a critical semilinear polyharmonic equation with the second boundary and with a non-negative perturbation.
利用弹性薄板的广义变分原理和双调和方程的特解序列，提出了一种求解圆板混合边值问题的数值方法。
The existence and the life span of solutions to some mixed initial-boundary value problems are also investigated.
文中不仅对数值求解双调和方程的两种不同方法作了介绍，还利用该方程生成了典型的H型、C型、O型网格。
It is not only introduced the two measures taken to solve the biharmonic equations, but the topical grids of H-type, C-type, and O-type are generated with this equation.
根据二维双调和方程的特点并借助于MATHEMATICA软件，得到了应力函数双调和方程的多项式解答。
According to the nature of two-dimensional biharmonic equations, this paper obtains a polynomial solution of the biharmonic equation for stress function by means of the MATHEMATICA software.
摘要利用由三角级数和幂级数复合构成的函数项级数的有关性质，得到了一类变系数非齐次调和方程边值问题的级数解。
In this paper by using the property of Fourier series a compound series consisting of trigonometric series and power series is established.
求解的方法是采用曲线坐标变换，两次求解相应的调和方程，推导出解的一般形式。然后利用边界条件确定通解中的待定常数。
The general solution for this plate is obtained by solving the corresponding harmonic equation twice with the help of the curvilinear coordinate transformation.
利用不动点理论，给出了一类半线性微分方程有界的调和伪概周期解存在的充分条件。
Using fixed point theorems, in this paper we give sufficient conditions of the existence of bounded mild pseudo almost periodic solution for some semilinear differential equations.
众所周知，分数次积分算子是调和分析中以偏微分方程为背景的一种重要算子。
It is well-known that fractional integral operator is one of the important operators in harmonic analysis with background of partial differential equations.
指数曲线方程、双曲线方程以及调和曲线方程常用来数学表达递减曲线。
Exponential, hyperbolic, and harmonic curve equations are often used to mathematically express the decline curve.
本文给出了某些二阶非线性微分方程在周期外力作用下存在调和解的若干定理。
In this paper we prove some theorems on harmonic solutions of some second-order nonlinear equations under a periodic external force.
计算中，在连续方程中增加了一个松弛项，将模式结果向已有实测调和常数的控制点推算潮高值趋近。
A relaxation term is added to the continuity equation to nudge the calculated sea levels to the sea levels predicted at gauging stations.
在本文中我们主要研究了等变调和映照、及其约化定理和等变变分公式，得到了等变调和映照的调和性方程。
In this paper, we mainly study equivariant harmonic maps, the theorem of reduction, the equivariant variational formula, and the harmonic equation.
本文主要是要利用调和分析的方法讨论偏微分方程中的若干问题。
In this paper we prepare to consider several problems of the partial differential equations by the methods of harmonic analysis.
研究了二阶摆型振动方程奇调和解的存在性。
The existence of odd-harmonic solutions for a second order pendulum-type oscillation equation was studied.
将控制方程的线性化与调和平衡法组合起来，建立周期及周期解的解析逼近公式。
By combining the linearization of the governing equation with the method of harmonic balance, we have established analytical approximate formulas for the period and the periodic solution.
将控制方程的线性化与调和平衡法组合起来，建立周期及周期解的解析逼近公式。
By combining the linearization of the governing equation with the method of harmonic balance, we have established analytical approximate formulas for the period and the periodic solution.
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