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A permeable tensor evolution equation of equivalently continuous medium has also been developed. 基于岩体裂隙的损伤变形，提出了裂隙岩体渗透张量演化方程。
In the article we show the decay of the solution for some nonlinear evolution equation of second order by using a difference inequality. 本文应用一个差分不等式证明了一类二阶非线性发展方程初边值问题整体解的衰减性质.
The major contents in this paper include: the exact solutions of the non-linear evolution equation and the integrable system. 本文研究的内容主要包括两个方面：非线性发展方程的精确解与可积系统。
The paper studies the global existence, asymptotic behavior and blowup of weak solutions to the initial bounary value problem of a nonlinear evolution equation. 摘要研究一类非线性发展方程初边值问题整体弱解的存在性、渐近性和解的爆破问题。
The advantages are via immunity operation to maintain diversity of the antibodies, and the speed of convergent are improved by using evolution equation. 算法的主要特点是利用免疫处理操作，提高种群的多样性，利用进化方程提高收敛速度。
Finally, they take advantage of the fixed point method for some contraction mapping and get the solvability of the inverse problem for the evolution equation. 最后，利用压缩映射不动点方法，得到反问题的可解性.
For the computational stability of linear evolution equation, the condition of CLF for judging the computational stability of initial value problem is introduced. 针对线性发展方程的计算稳定性问题，介绍了判定线性发展方程初值问题的稳定性判别条件：CLF条件。
According to basic damage principle, the shear damage variable of rock and the pull damage variable of grout body are defined, and the damage evolution equation is suggested. 摘要根据损伤理论的基本原理，分别定义了岩体剪切损伤变量和受拉浆体材料的损伤变量，确定了各自相应的损伤演化方程；
YANG Zhijian,SONG Changming.On the existence and nonexistence of global solutions for a class of nonlinear evolution equation[J].Acta Math Appl Sinica,1997,20(3):321-331. [9]杨志坚;宋长明.;关于一类非线性发展方程整体解的存在性问题[J]
Indeed, it is not clear whether one should interpret the Dirac equation as a quantum mechanical evolution equation, like the Schrodinger equation for single particle. 而时下一部理论的发展，一种数学语言是不可缺少的，只要人们试图潜心地思考和研究物理学问题及物理现象。
First, by virtue of semigroup theory, the considered system is converted into an evolution equation in abstract space and the uniqueness of the solution to the evolution equation is proved. 首先将所讨论的系统化为抽象空间中的发展方程;并利用Co半群理论给出闭环系统解的存在唯一性.
Three eigenvalue problems associated with the same isospectral evolution equation are proposed. The corresponding nonlinearized eigenvalue problems and their relations are studied by the reduction procedure. 摘要通过约化理论，研究了对应于同一离散孤立子方程族的三个离散特征值问题的非线性化特征值问题以及它们之间的关系。
It is shown that at the high-frequency limit, the evolution of the wave is governed by a nonlinear evolution equation, which is an extension of the well-known Benjamin-Ono equation. 在高频率假设下,分析得到控制波的演化的非线性方程,且该方程是著名的Benjamin-Ono方程的推广,并对新的方程进行了数值计算,得到简单孤立波解。
By setting up a basic evolution equation, analyses the operating mechanism and characters of the system in terms of non-stability, diversity (bifurcation), catastrophe and random fluctuation. 建立了系统的基本演化方程，并据此分析说明了知识创新系统的不稳定性、多样性、分岔、突变以及随机“涨落”等特征和作用机制。
In order to choose rock cover of Xiamen subsea tunnel now,3D elastoplastic constitutive relation and damage evolution equation for 4 profiles has been done along the longitudinal of the tunnel. 在厦门海底隧道轴线的地质剖面图上,选取了4个典型的剖面,应用多裂隙岩体三维弹塑性本构关系和损伤演化方程进行数值分析研究,得到了应力分布、洞周位移、塑性区、损伤区等结果。
Furthermore, the global minimum of the error function is verified to be the terminal attractor of the error evolution equation, which guarantees the NNs learning process converge within finite time. 且最优值点即是误差演化方程的终端吸引子，从而又保证了网络的学习过程能在有限时间内产生收敛。
The nonexistence of global weak solution to elliptic equation and the evolution equation, together with the nonexistence of local weak solution to hyperbolic equation is contained in this paper. 本文运用试验函数法研究了带有非局部源的偏微分方程的全局弱解的不存在性，内容包括椭圆方程、发展方程全局解的不存在性以及双曲型方程的局部弱解的不存在性。
The extended homogenous balance method is applied to find solitary wave solutions of nonlinear evolution equations. 摘要为了求非线性发展方程的孤立波解，提出了齐次平衡法的扩展应用。
In this thesis, we study systematically and allsidedly soliton perturbation theory for a sort of nonlinear evolution equations. 本文系统地、全面地研究了一类重要的非线性演化方程的孤子微扰问题。
M. J. Ablowitz and P. A.Clarkson,Solitons，Nonlinear Evolution Equations and Inverse Scattering，Cambridge University Press, 1991. 刘式适，刘式达编著，物理学中的非线性方程，2000第一版，北京大学出版社。