PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.     

Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method北大核心CSCD

Based on the homotopy analysis method, the nonlinear vibration of porous functionally graded material (FGM) conveying pipes under generalized boundary conditions was studied. Based on the power-law distribution of the FGM and the Voigt model, the physical properties of the porous pipe material were described. Under the Euler-Bernoulli beam theory and the von Kármán nonlinear theory, and by means of Hamilton’s variational principle, the dynamic control equations and generalized boundary conditions for porous FGM conveying pipes were established. The homotopy analysis method was used to solve the nonlinear vibration characteristics of the porous FGM conveying pipe under generalized boundary conditions. The numerical results show that, the translation spring has little effect on the critical velocity of instability, while the rotation spring increases the critical velocity of instability, making the system more stable; in the nonlinear system, the viscoelastic coefficient does not change the critical velocity; the pipe length, the power-law exponent and the porosity all influence the nonlinear free vibration of the porous FGM conveying pipe. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Linear low-rank approximation and nonlinear dimensionality reduction

We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of column-partitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.     

增生映射的扰动理论对与广义(p,q)-Laplace算子相关的非线性椭圆系的应用

Using perturbation results on the sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present some abstract results for the existence of the solutions of nonlinear Neumann elliptic systems which is related to the so-called generalized （p, q）-Laplacian in this paper. The systems discussed in this paper and the method used extend and complement some of the previous work.     

Global existence and blow-up of solutions to a nonlocal evolution p-laplace system with nonlinear boundary conditions

In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.     

Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method北大核心CSCD

Application of the wavelet Galerkin method (WGM) to numerical solution of nonlinear buckling problems was studied with classical elastic thin rectangular plates. First, the discretized scheme of the von Kármán equation were introduced, then a simple calculation approach to the Jacobian and Hessian matrices based on the WGM was proposed, and the wavelet discretized scheme-based eigenvalue equation method, the extended equation method and the pseudo arc-length method for nonlinear buckling analysis were discussed. Second, the secondary post-buckling equilibrium paths of elastic thin rectangular plates and the effects of aspect ratios, boundary conditions and bi-directional compression on the mode jumping behaviors, were discussed in detail. Numerical results show that, the WGM possesses good convergence for solving buckling loads on rectangular plates, and the obtained equilibrium paths are in good agreement with those from the stability experiments, the 2-step perturbation method and the nonlinear finite element method. Given the feasibility of combination with different bifurcation computation methods, the WGM makes an efficient spatial discretization method for complex nonlinear stability problems of typical plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

含有p拉普拉斯算子方程的解的存在性研究

By using the perturbation theories on sums of ranges for nonlinear accretive mappings of Calvert and Gupta (1978), the abstract result on the existence of a solution u ∈ Lp (Ω) to nonlinear equations involving p-Laplacian operator △p, where 2N/N 1 ＜ p ＜ ∞ and N (≥ 1 )denotes the dimension of RN,is studied. The equation discussed and the methods shown in the paper are continuation and complement to the corresponding results of Li and Zhen's previous papers. To obtain the result ,some new techniques are used.     

A FEASIBLE DIRECTION ALGORITHM WITHOUT LINE SEARCH FOR SOLVING MAX-BISECTION PROBLEMS

This paper concerns the solution of the NP-hard max-bisection problems. NCP func-tions are employed to convert max-bisection problems into continuous nonlinear program-ming problems. Solving the resulting continuous nonlinear programming problem generatesa solution that gives an upper bound on the optimal value of the max-bisection problem.From the solution, the greedy strategy is used to generate a satisfactory approximate so-lution of the max-bisection problem. A feasible direction method without line searches isproposed to solve the resulting continuous nonlinear programming, and the convergenceof the algorithm to KKT point of the resulting problem is proved. Numerical experimentsand comparisons on well-known test problems, and on randomly generated test problemsshow that the proposed method is robust, and very efficient.     

A Reaction-diffusion system with nonlinear absorption terms and boundary flux

This paper deals with a reaction-diffusion system with nonlinear absorption terms and boundary flux. As results of interactions among the six nonlinear terms in the system, some sufficient conditions on global existence and finite time blow-up of the solutions are described via all the six nonlinear exponents appearing in the six nonlinear terms. In addition, we also show the influence of the coefficients of the absorption terms as well as the geometry of the domain to the global existence and finite time blow-up of the solutions for some cases. At last, some numerical results are given.     

非线性Schroeding方程Cauchy问题解的Blow—Up的质量集中

We prove in this paper the blow-up theorem of the generalized solution.and its L^2 mass concentration theorem on the set of blow-up points near the blow-up time of the Cauchy problem for nonlinear Schroedinger equations and give the structure of the set of the blow-up points and the estimates on the blow-up time.Furthermore we extend and improve some results in [2] and [5].     

关于含有p拉普拉斯算子方程解的存在性的注

利用Calvert和Gupta关于非线性增生映射值域之和的扰动定理,得到了一类含有p拉普拉斯算子Δp的非线性Neumann边值问题在Lp(Ω)空间中解的存在性的结论,其中2N/(N 1)相似文献   

与p-Laplace算子方程相关的m增生映射的零点集的构造

许多求非线性系统的均衡解的问题都可以转化为寻找某个m增生映射的零点的问题.将利用非线性增生映射的性质,给出一类与p-Laplace算子方程相关的m增生映射的零点集的构造,其中2N/N+1p+∞且N≥1.     

Sensitivity analysis for parametric completely generalized nonlinear implicit quasivariational inclusions

In this paper we introduce a new class of parametric completely generalized nonlinear implicit quasivariational inclusions and study the behavior and sensitivity analysis of the solution set of the parametric completely generalized nonlinear implicit quasivariational inclusion dealing with multivalued and single-valued nonlinear mappings in Hilbert spaces. Our results extend, improve and unify the previously many known results in this area.     

非线性映射在有界区域内零点数目的若干结果

本文利用连续同伦方法讨论非线性映射在有界区域内零点的存在性和零点数目,以及推广若干经典定理。     

对非线性椭圆边值问题解的存在性的研究

利用非线性增生映射值域的扰动定理 ,研究了非线性椭圆边值问题 ( @)在 L2 (Ω )中解的存在性 .( @) -△pu +g( x,u) =f a.e.在Ω中-〈v,| u|p- 2 u〉∈βx( u( x) ) a.e.在Γ上其中 f∈ L2 (Ω )给定 ,Ω RN,N 1 ,△ pu=div( | u|p- 2 u)为 P拉普拉斯算子 ,1 2 NN +1 ,v为 Γ的外法向导数 ,g:Ω× R→ R满足 Caratheodory条件 ,对 x∈ Γ,βx是正常、凸、下半连续函数 φx=φ( x,· )的次微分 ,其中 φ:Γ×R→ R.     

Convergence analysis of a nonlinear Lagrange algorithm for general nonlinear constrained optimization problems

The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.     

一类非线性椭圆边值问题解的存在性

目前 ,对 s——拉普拉斯算子△s的研究是较为活跃的数学课题 .原因在于算子 -△s与许多物理现象有关 .比如 :反射扩散问题 ,石油提取问题等等 .基于此因 ,在文 [3]的基础上 ,我们将继续研究以下非线性边值问题在 Ls(Ω) ,( 1 2 nn+1 )中解的存在条件 .-△su +g( x,u) =f几乎处处在Ω中-〈 ,| u|s- 2 u〉 =0几乎处处在Γ上其中 f∈Ls( Ω)给定 ,Ω Rn( n 1 ) ,△su=div( | u|s- 2 u) ,g∶Ω× R→ R满足 Caratheodory条件 .本文把文 [3]关于非线性边值问题 @在 Lp( Ω) ( 2 p<+∞ )空间中解的存在性的研究推广到 Ls( Ω) ( 1 2 nn+1 )空间中 .     

一类无Lipschitz假设的非线性算子的带误差的Ishikawa迭代程序

１引言与预备知识 设Ｘ为一实赋范线性空间．Ｘ·是Ｘ的对偶空间,正规对偶映射Ｊ：Ｘ→２Ｘ定义为：其中＜·,·＞表示Ｘ和Ｘ的广义对偶组．由［１］知若Ｘ是一致光滑Ｂａｎａｃｈ空间,则Ｊ（·）单值且在Ｘ的任何有界子集上为一致连续．我们用ｊ（·）表示单值的正规对偶映射． 定义１［２］设Ｋ是Ｘ的一非空子集,算子Ｔ：Ｋ→Ｘ称为是　－强伪压缩的,如果存在一个严格增加函数　,存在使得 定义２［２,３］Ｔ称为　强增生算子的,如果（Ｉ－Ｔ）是　－强伪压缩算子（其中Ｉ是恒等算子）． 若定义１（相应地;定义２）中　（ｔ）＝ｋ…     

Constrained open mapping theorem with applications

We prove a generalization of Graves? Open Mapping Theorem for a class of mappings which can be approximated at a reference point by a set-valued one having particular properties. The nonlinear mapping is restricted to a closed convex subset of a Banach space. We apply the results to derive necessary and sufficient conditions ensuring the existence of a differentiable selection for the inverse mapping. A slight generalization of a sufficient condition by J. Klamka on so-called constrained exact local controllability of nonlinear and semi-linear dynamic systems is also proved.     

广义p-Laplace算子相关的非线性边值问题解的存在性

本文首先把p-Laplace算子推广为广义p-Laplace算子,然后利用非线性增生映射值域的扰动理论研究了与广义p-Laplace算子相关的具有牛曼边值的非线性椭圆问题在LP(Ω)空间中解的存在性,其中2≤p< ∞．本文所讨论的方程及所用的方法是对以往一些工作的补充和延续．