多维拟线性退化抛物方程Cauchy问题解的唯一性和稳定性

本文证明了拟线性退化抛物方程 (e)u/(e)t=n∑i=1 (e)/(e)xi(aij(u)(e)u/(e)xi)+n∑i=1 (e)bi(u)/(e)xi -c(u), u(x,0)=u0(x),aij(u)ξiξj≥0,(A)ξ∈Rn 的Cauchy问题BV解的唯一性和稳定性.     

带有临界增长的Kirchhoff型问题的基态解

本文主要考虑如下Kirchhoff问题{-(a+b∫R_3|?u|~2dx)?u+u=f(x,u)+Q(x)|u|~4u,u∈H~1(R~3),其中a,b是正的常数.我们证明了基态解,即上述问题的极小能量解的存在性.同时,如果假定Q≡1,且h(x)满足一定的条件,可以证明下述问题{-(a+b∫R_3|?u|~2dx)?u+u=|u|~4u+h(x)u,u∈H~1(R~3)的基态解的存在性.     

p—函数的最大值问题

以■记全体标准p-函数,设固定p_0∈■且0相似文献   

三阶非线性特征值问题解的存在性

利用锥不动点指数研究了三阶非线性特征值问题u+ρ3u=λg(t)f(u),00.     

INFINITELY MANY SOLUTIONS FOR AN ELLIPTIC PROBLEM INVOLVING CRITICAL NONLINEARITY

We study the following elliptic problem:{-div(a(x)Du)=Q(x)|u|2-2u+λu x ∈Ω ,u=0 on ΩUnder certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method.     

人口问题中广义三维GINZBURG-LANDAU模型方程

本文讨论三维广义Ginzburg-Landau模型方程的初边值问题ut=-a1↓△^4u a2↓△^2u ↓△^2g(u) G(u),σu/σv=0,σ△u/σv=0,u(x,0)=u0(x)解的整体存在性、唯一性、渐近性质和爆破。     

一类带导数项的非线性特征值问题正解的存在性

应用 Schauder不动点定理 ,证明了带导数项的非线性特征值问题 :　　 u″+λa( t) f ( u,u′) =0 ,0 0充分小 ,f :[0 ,∞ )× R→ R连续且 f( 0 ,0 ) >0 .     

非线性三点共轭边值问题正解存在性的特征值准则

本文提出了三点边值问题-v″(t)=b(t)f(v(t)),满足v′(0)=0及v(1)=αv(η)的共轭问题-u″(t)=b(t)f(u(t)),u′(0)=u(1)=0及u′_+(η)-u′_-(η)=αu′(1),得到了相应的Green函数．将其转化为Hammertein型积分方程,借助于其相应线性问题的第一特征值,利用锥上的不动点指数理论,给出了共轭问题单个正解及多个正解存在的特征值准则．     

非线性Neumann问题正解的存在性

研究非线性Neumann问题(p(t)u′)′+q(t)u=f(t,u),t∈(0,1),u′(0)=u′(1)=0正解的存在性,其中p,q∈C[0,1]满足p(t)>0,0*,t∈[0,1],b*,t∈[0,1],b^*为线性问题(p(t)u′)′+bu=0,u′(0)=0,u(1)=0的第一特征值.运用拓扑度理论及Rabinowitz全局分歧定理为上述问题建立了正解的存在性结果.     

四阶非线性特征值问题的正解

本文考虑了四阶非线性特征值问题d4u/dt4=λg(t)f(u,u″),0＜t＜1,u(0)=u(1)=0,au″(0)-bu″′(0)=0,cu″(1)+du″′(1)=0.其中g(t)∈C((0,1),[0,∞)),f(u,v)∈C([0,∞)×(-∞,0],[0,∞)),a≥0,b≥0,c ≥0,d ≥ 0,且△=ac+ad+bc＞0.利用锥压缩与拉伸不动点定理,获得了上述问题正解的存在性结果.     

杜芬方程的1／3纯亚谐解及其过渡过程

通过谐波平衡法和数值积分法研究了杜芬方程的1／3纯亚谐解,对参数变化的过渡过程的敏感性和扰动初始值的过滤进行了研究,同时,还对谐波平衡法和数值积分法的精度进行了比较,也考虑了亚谐波成分的渐近稳定性。     

A numerical approach for solving an extended Fisher-Kolomogrov-Petrovskii-Piskunov equation

In the present paper a numerical method, based on finite differences and spline collocation, is presented for the numerical solution of a generalized Fisher integro-differential equation. A composite weighted trapezoidal rule is manipulated to handle the numerical integrations which results in a closed-form difference scheme. A number of test examples are solved to assess the accuracy of the method. The numerical solutions obtained, indicate that the approach is reliable and yields results compatible with the exact solutions and consistent with other existing numerical methods. Convergence and stability of the scheme have also been discussed.     

A regularization-stabilization technique for nonlinear conservation equation computations

A regularization procedure for nonlinear conservation equations is introduced and demonstrated to have a stabilizing effect on the numerical solution of the associated approximate problem. Representative results for a least-squares finite-element method are given, and the numerical performance of the stabilization procedure explored. The effect of the regularization term is similar to a local numerical dissipation dependent on the numerical itegration time step.     

A NUMERICAL PERTURBATION EXPANSION METHOD FOR THE SOLUTION OF A LIENARD-TYPE INITIAL-VALUE PROBLEM WITH PERIODIC DECAYING FORCING TERM

A numerical perturbation expansion method is developed, analysed and implemented for the numerical solution of a second-order initial-value problem. The differential equation in this problem exhibits cubic damping, a cubic restoring force and a decaying forcing-term which is periodic with constant frequency. The method is compared with the numerical method by Twizell [1]. In fact, the later is first perturbation approximate solution in the present paper.     

求解非线性互补问题的微分方程方法

本文构造了一种求解非线性互补问题的微分方程方法.在一定条件下,证明了微分方程系统的平衡点是非线性互补问题的解并且基于一般微分方程系统的数值积分建立了一个数值算法.在适当的条件下,证明了此算法产生的序列解是收敛的.本文最后给出了数值结果,该结果表明了此微分方程方法的有效性.     

A scheme for stable numerical differentiation

A method for stable numerical differentiation of noisy data is proposed. The method requires solving a Volterra integral equation of the second kind. This equation is solved analytically. In the examples considered its solution is computed analytically. Some numerical results of its application are presented. These examples show that the proposed method for stable numerical differentiation is numerically more efficient than some other methods, in particular, than variational regularization.     

A control problem related to wastewater treatment

The management of a wastewater treatment system is studied as a pointwise control problem with state constraints. A theoretical analysis of the problem is developed, a numerical algorithm is proposed and numerical results are given.     

微分代数问题的一类数值算法

其中y和f的维数为l,u和g的维数为m.假定函数f和g具有如下要求的连续导数且矩阵g_y(y)f_u(t,y,u)具有有界逆矩阵,即存在M>0,使‖(g_y(y)f_u(t,y,u))~(-1)‖≤M.     

A LEAP FROG FINITE DIFFERENCE SCHEME FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS OF HIGHORDER

1.IntroductionItiswellknowthatthenonlinearequationsofSchr6dingertypeareofgreatimportancetophysicsandcanbeusedtodescribeextensivephysicalphenomenatll.InthispapergwewillconsidertheperiodicinitialvalueproblemforthefollowingclassofnonlinearSchrodingerequationofhighorder:wherem',MandMIareallpositiveconstant.Inthepaper[2])therehavediscussedinitialValueproblemofsystemsuchas(1.1)(1.3),introducedadifferenceschemeofconservationtype,andresearcheditsstabilityandconvergence.Otherwise,itisanimplicitmetho…     

A novel variable‐order fractional nonlinear Klein Gordon model: A numerical approach

In this article, a novel variable order fractional nonlinear Klein Gordon model is presented where the variable‐order fractional derivative is defined in the Caputo sense. The merit of nonstandard numerical techniques is extended here and we present the weighted average nonstandard finite difference method to study numerically the proposed model. Special attention is paid to study the convergence and to the stability analysis of the numerical technique. Moreover, the truncation error is analyzed. Three test examples are provided. Comparative studies are done between the used numerical technique and the weighted average finite difference method. It is found that the stability regions are larger by using the weighted average nonstandard finite difference method.