一类交叉耦合非线性反应扩散方程组的爆破分析

主要研究了具有混合型的多重非线性项的抛物方程组的初边值问题.方程组中的非线性项是幂函数和指数混合型的.这些非线性项组合出了源-流交叉耦合,通过比较原理得到了方程组的上下解,并得到了解有限时刻爆破的临界指标.     

具有渐进非线性项的Kirchhoff型方程的正解（英文）

本文研究一类非线性Kirchhoff型方程.非线性项函数f(x, u)在无穷远处关于u是渐进线性或渐进非线性的.若位势函数V (x)和非线性项f(x, u)满足给定的条件,本文在工作空间缺乏紧性嵌入的情形下获得该方程正解的存在性.     

基于纵荡速度的非线性变参数无人艇模型

无人艇的水动力学具有强非线性与时变性,为便于转艏控制,提出一种基于纵荡速度的非线性变参数(nonlinear parameter varying,NPV)模型.首先从水动学机理出发,引入Ross阻尼模型,建立三自由度的非线性机理模型.其次,在机理模型基础上,将非线性项隐含于线性结构中,使模型构成类线性结构,再忽略数值较小的横荡阻尼项,并以纵荡速度为变参数,建立基于纵荡速度的NPV模型.NPV模型结构简单,具有非线性项与变参项,为Norrbin非线性模型与线性变参数(linear parameter varying,LPV)模型的扩展形式.最后,由仿真和实验验证了NPV模型能够很好地刻画无人艇转艏运动的非线性与时变特性.     

两端固定的奇异梁方程的多重正解

设 n 是一个任意的自然数. 证明了一个两端固定的奇异梁方程的 n 个正解的存在性, 其中非线性项是一个Carathéodory 函数. 主要工具是涉及非线性项的高度函数与锥压缩锥拉伸型的 Krasnoselskii不动点定理. 进一步的研究表明,如果非线性项在零点和无穷远处的增长极限均为无界函数, 该方程仍可能具有正解.     

带跳跃非线性项的p-Laplacian问题的结点解

研究了带跳跃非线性项的p-Laplacian方程结点解的存在性.如果该问题的非线性项跨越其对应齐次问题的Fucik谱,我们证明了该问题至少存在一个结点解.     

关于一个非线性几何光学中的非严格双曲守恒律系统的研究

研究了一个产生于非线性几何光学中的非严格双曲守恒律系统.该系统具有强非线性流函数项,且狄拉克激波可能同时出现在解的两个状态变量中.通过未知函数的一个变换,该系统的非线性流函数项得到弱化,从而其黎曼问题被完全解决.     

一类非线性Keller-Segel方程的局部零能控性

该文研究一类由抛物方程和椭圆方程耦合的非线性Keller-Segel方程的局部零能控性.该方程不仅具有非线性的drift-diffuion项,而且具有非线性的人口增长项.作者利用抛物-椭圆结构的非局部特性将方程组化为单个非线性抛物型方程并利用Kakutani不动点定理证明了局部零能控性的存在性.     

具有惯性项和阻尼项的Cahn-Hilliard方程的整体吸引子

本文研究具有惯性项和阻尼项的亚三次非线性Cahn-Hilliard方程的初边值问题.在非线性弱正则的条件下,我们建立弱解的适定性,而不考虑非线性项的一阶导数的下界条件.接着利用弱解的渐近紧和能量解的严格Lyapunov函数的存在性,证明在空间(H~2(?)∩H_0~1(?))×L~2(?)上存在整体吸引子.     

一类非线性 Dirichlet 边值问题的正径向解

通过构造适当的锥并利用锥拉伸与锥压缩型的不动点定理研究了单位球上一类椭圆 Dirichlet 边值问题的正径向解的存在性, 其中非线性项可以是奇异的. 主要结论表明正径向解的存在性仅依赖于非线性项在其定义域的某个有界子集上的性质, 而与非线性项在此集合以外的性质无关.     

具时滞和记忆项的非线性粘弹性波动方程解的爆破——纪念阳名珠先生

本文研究一类具时滞和记忆项的非线性粘弹性波动方程的初边值问题.对初始条件、时滞项、记忆项、非线性源项和阻尼项附加适当的条件,利用凸性方法证明了能量解的爆破性,从而推广了已有文献的结果.     

用非线性方程组求解等式约束非线性规划问题的降维算法

本文研究线性和非线性等式约束非线性规划问题的降维算法.首先,利用一般等式约束问题的降维方法,将线性等式约束非线性规划问题转换成一个非线性方程组,解非线性方程组即得其解;然后,对线性和非线性等式约束非线性规划问题用Lagrange乘子法,将非线性约束部分和目标函数构成增广的Lagrange函数,并保留线性等式约束,这样便得到一个线性等式约束非线性规划序列,从而,又将问题转化为求解只含线性等式约束的非线性规划问题.     

Nonlinear Separation Approach to Constrained Extremum Problems

In this paper, by virtue of a nonlinear scalarization function, two nonlinear weak separation functions, a nonlinear regular weak separation function, and a nonlinear strong separation function are first introduced, respectively. Then, by the image space analysis, a global saddle-point condition for a nonlinear function is investigated. It is shown that the existence of a saddle point is equivalent to a nonlinear separation of two suitable subsets of the image space. Finally, some necessary and sufficient optimality conditions are obtained for constrained extremum problems.     

Metric nonlinear connections

For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange metric. For the particular case when the system of SODE and the metric structure are Lagrangian, we prove that the canonical nonlinear connection of the Lagrange space is the only nonlinear connection which is metric and compatible with the symplectic structure of the Lagrange space. For this particular case, the metric tensor determines the symmetric part of the canonical nonlinear connection, while the symplectic structure determines the skew-symmetric part of the nonlinear connection.     

非线性时变广义分布参数系统的适定性问题

本文的主要目的是讨论非线性时变广义分布参数系统的适定性问题.首先,在Banach空间中引入由连续(可能是非线性的)算子引导的非线性广义发展算子,该非线性广义发展算子是广义发展算子的推广,并研究非线性广义发展算子的性质;然后,应用非线性广义发展算子讨论非线性时变广义分布参数系统的适定性问题,并给出解的构造性表达式.     

Analysis of the nonlinear vibration of a two-mass–spring system with linear and nonlinear stiffness

An analytical approach is developed for areas of nonlinear science such as the nonlinear free vibration of a conservative, two-degree-of-freedom mass–spring system having linear and nonlinear stiffnesses. The main contribution of this research is twofold. First, it introduces the transformation of two nonlinear differential equations for a two-mass system using suitable intermediate variables into a single nonlinear differential equation and, more significantly, the treatment of a nonlinear differential system by linearization coupled with Newton’s method. Secondly, the major section is the solving of the governing nonlinear differential equation where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using a first-order variational approach. The aforementioned approach proposed by J.H. He, who actually developed the method, is exactly He’s variational method. This approach is an explicit method with high validity for resolving strong nonlinear oscillation system problems. Two examples of nonlinear two-degree-of-freedom mass–spring systems are analyzed, and verified with published results and exact solutions. The method can be easily extended to other nonlinear oscillations and so could be widely applicable in engineering and science.     

Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-Burmeister NCP Functions

This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.     

Nonlinear separation approach to inverse variational inequalities

In this paper, we employ the image space analysis to investigate an inverse variational inequality (for short, IVI) with a cone constraint. By virtue of the nonlinear scalarization function commonly known as the Gerstewitz function, three nonlinear weak separation functions, two nonlinear regular weak separation functions and a nonlinear strong separation function are first introduced. Then, by these nonlinear separation functions, theorems of the weak and strong alternative and some optimality conditions for IVI with a cone constraint are derived without any convexity. In particular, a global saddle-point condition for a nonlinear function is investigated. It is shown that the existence of a saddle point is equivalent to a nonlinear separation of two suitable subsets of the image space. Finally, two gap functions and an error bound for IVI with a cone constraint are obtained.     

求解2—D波动方程系数反问题的迭代方法及收敛性

本文针对地震勘探中提出一类重要的２－Ｄ波动方程反演问题，通过定义一个新的非线性算子将２－Ｄ波动方程的反演问题归结为一个新的非线性算子方程，详细讨论了非线性算子的性质，给出了求解反问题的迭代方法，并证明了这种迭代方法的收敛性。     

一类模糊非线性方程组及解法

模糊非线性方程组 ,在模糊控制和现实生活中很普遍 .本文考虑一类模糊非线性方程组的性质 ,然后给出一种解法 .首先把模糊非线性方程组转变成非线性规划 ,再用非线性规划中的方法或软件来解 .