非线性偏微分方程

非线性偏微分方程之间的Miura变换

The Miura transformation between nonlinear partial differential equations

建立了中空纤维膜接触器的传质模型，应用MATLAB处理了传质模型中的非线性偏微分方程组，预测了CO2出口浓度。

The mathematical model of mass transfer in the membrane absorber was derived . The solution method for nonlinear partial differential equations was given by using MATLAB . CO_2 concentration in liquid outlet was predicted by mathematical model of kinetics of mass transfer .

Jacobi椭圆函数展开法在求解非线性偏微分方程组中的应用

Applications of Expansion Method About the Jacobi Elliptic Function of Nonlinear Partial Differential Equations

Jacobi椭圆函数在求解非线性偏微分方程（组）中具有重要作用。

Jacobi elliptic function is very useful for solving nonlinear partial differential equation ( s ) .

本文主要探讨了格子Boltzmann方法在模拟非线性偏微分方程方面的一些应用。

In this thesis , we discuss applications of simulating some Nonlinear Partial Differential Equations by the lattice Boltzmann Method .

若干非线性偏微分方程的格子BGK模拟

Simulation of Lattice BGK Models for Some Nonlinear Partial Differential Equations

通过将位移和载荷展开为Fourier级数，把非线性偏微分方程组转化为二阶常微分方程组，并可由四阶Runge-Kutta方法数值求解。

The nonlinear partial differential equations obtained are transformed into ordinary differential equations by expansion into Fourier series and then solved numerically by the Runge-Kutta method of the fourth order .

本文由虚功原理建立弹性圆拱的平衡方程，用有限差分法对非线性偏微分方程组进行求解（Park法对时间进行差分）。

The equilibrium equations of elastic circular arches are established using the principle of virtual work . The nonlinear partial differential equations of motion are solved using a finite difference method ( Park 's method for time difference ) .

本文对非线性偏微分方程（PDE）间断有限元方法（DG）的误差分析以及后处理技术进行了研究，内容主要由作者博士期间所有发表及提交的学术论文构成。

The priori error analysis and post-processing technique for the discontinuous Galerkin ( DG ) methods for nonlinear partial differential equations ( PDEs ) have been studied in the present thesis .

我们将能量Casimir方法与现代非线性偏微分方程理论中的非线性先验估计方法有创新性地结合起来，在该领域取得了突出的成果。

The author and his research group have combined the Energy Casimir method with the a prior estimate method innovatively and have attained outstanding achievements .

由于该方程是非线性偏微分方程，不易求解，因此采用Legendre变换将其转换成对偶问题进行研究。

This equation is non-linear partial differential equation , yet it is difficult to solve it , this paper change primary problem to the dual problem by using Legendre transform .

用级数展开把非线性偏微分方程组化为易于求解的Kronecker张量积形式的二阶常微分方程组，并由四阶Runge-Kutta法数值求解。

The nonlinear partial differential equations are transformed into the ordinary differential equations of Kronecker tensor product by series expansion and solved numerically by the fourth order Runge Kutta method .

通过假设强迫振动的组合谐响应模式，采用Kantorovich时间平均法，把非线性偏微分方程化成了非线性常微分方程组。

Assuming that the vibration is harmonic and using Kantorovich time averaging method , the partial differential equations are converted into a system of nonlinear ordinary differential equations .

这个算法也可用于解其他的非线性偏微分方程，如变更Boussinesq方程组、非线性浅水长波近似方程组等。

The method can also be applied to solve some other systems of nonlinear partial differential equations , such as variant Boussinesq and the nonlinear approximate equations for long wave in shallow water .

对凸体理论中的一类二阶完全非线性偏微分方程的正解给出了C1先验估计。

The authors in this paper get a C ~ 1 apriori estimate for the positive k-convex solutions of some fully nonlinear second order partial differential equation , which arises in the convex bodies theory .

讨论一类具有连续分布滞量的二阶非线性偏微分方程在Robin，Dirichlet边界条件下解的振动性，利用Green定理及微积分技巧，获得该类方程解振动的充分条件。

It is discussed that the oscillation of a class of second order nonlinear partial differential equations with continuous distribution delay under Robin and Dirichlet boundary value conditions . The sufficient conditions for the oscillation of solutions of the equation are obtained by using Green 's theorem and calculus techniques .

主要利用Jacobi椭圆函数所满足的方程并用其解代替Jacobi椭圆函数以求非线性偏微分方程的周期解，并举例说明该方法的应用。

The main idea of this method is to take full advantage of the elliptic equation that Jacobi elliptic functions satisfy and use its solutions to replace Jacobi elliptic functions in Jacobi elliptic function method . Some illustrative equations are investigated by this means .

基于多尺度分析和Galerkin方法，提出了一类改进非线性偏微分方程的已知逼近解精度的线性化修正方法.通过误差分析和数值例子说明了方法的有效性。

A linearized modifying algorithm based on multi-resolution analysis and wavelet - Galerkin method is proposed , which can be used to improve the precision of the approximate solution of nonlinear partial differential equations . Error estimates and the numerical examples indicate the effectiveness of the proposed algorithm .

由于数学模型主要是非线性偏微分方程，且各方程耦合很紧密，因此采用数值方法进行离散求解。本文分别采用FLUENT的有限体积法和COMSOL的有限元法来求解数学模型。

Since the mathematical model is nonlinear partial differential equations , and each equation is closely coupled , therefore discretized and solved by numerical methods , the mathematics model solved by finite volume method of FLUENT and finite element method of COMSOL in this paper .

首次将Jacobi椭圆函数展开法应用于求解非线性偏微分方程组，以变异的Boussinesq方程为例演示了方法的有效性，用此方法求出的精确周期解包含了冲击波解。

Expansion method about the Jacobi elliptic function is firstly applied to systems of nonlinear partial differential equations . The variant Boussinesq equation is considered to illustrate the effectiveness of the method . The periodic solutions are obtained by the method , including the shock wave solutions .

用一个未知函数的变换将（n+1）维Sine-Gordon方程转化为新未知函数及其偏导数为变元的多项式型的非线性偏微分方程。

By means of a transformation of unknown function , the ( n + 1 ) - dimensional Sine-Gordon equation was converted into a nonlinear partial differential equation of a polynomial type with a new unknown function and its partial derivatives .

由于SFS方法本身是对一个病态的非线性偏微分方程进行求解，所以在求解过程中需要增加光强约束条件、表面光滑约束条件和表面可积性约束条件，使之转变为可以迭代求解的问题。

Because the SFS method is to resolve an ill-conditioned PDE , some necessary constraint conditions , such as the brightness constraint , the smoothness constraint and the integrability constraint , etc. , have to be added to convert this equation to a calculable one .

首先用行波变换将非线性偏微分方程转化为非线性常微分方程，然后采用摄动方法直接求解该非线性常微分方程，最后求得了非线性Klein-Gordon方程的二级近似解。

In this paper , nonlinear partial differential equation is transformed to nonlinear ordinary differential equation by virtue of traveling wave transformation method , and then straightforwardly solve it by taking advantage of perturbation method . Finally , the second order approximate solutions of nonlinear Klein-Gordon equation are successfully obtained .

并研究了非线性偏微分方程组的解在正则部分的情形。

The case of regular solutions of nonlinear PDAEs is investigated .

几个非线性偏微分方程的非古典对称及相似解

Nonclassical symmetries and similarity solutions of some nonlinear partial differential equations

两类非线性偏微分方程的新的精确解

New Exact Solutions of Two Kinds of Nonlinear Partial Differential Equations

各向异性扩散方程是一种非线性偏微分方程模型。

Anisotropic diffusion equation is a non-linear partial differential equations model .

非线性偏微分方程的极大原理和解的爆破

Maximum Principles and Blow-up of Solutions for Nonlinear Partial Differential Equations

一非线性偏微分方程的相似性解方程

Equation of Similarity Solution for a Non - linear Partial Differential Equation

含有δ函数的弱非线性偏微分方程的摄动解

Perturbation Solution of the Weak-Nonlinear Partial Differential Equation with 5-Function