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ASYMPTOTIC ESTIMATION FOR SOLUTION OF A CLASS OF SEMI-LINEAR ROBIN PROBLEMS 认领 引用
1
作者 Cheng Ouyang 《Analysis in Theory and Applications》 2005年第4期311-316,共6页
A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic exp... A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution. 展开更多
关键词 semi-linear singular perturbation Robin problem asymptotic expansion
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DIAGONALIZATION METHOD FOR A SINGULARLY PERTURBED VECTOR ROBIN PROBLEM 认领 引用
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作者 倪守平 《Applied Mathematics and Mechanics(English Edition)》 SCIE 1989年第4期329-336,共8页
In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic be... In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type. 展开更多
关键词 DIAGONALIZATION METHOD FOR A SINGULARLY PERTURBED VECTOR ROBIN PROBLEM
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A Robin Problem for Quasi-linear System 认领 引用 被引量：1
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作者 0UYANGCheng 《Chinese Quarterly Journal of Mathematics》 2004年第2期160-163,共4页
In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using... In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities. 展开更多
关键词 quasi-linear system Robin problem singular perturbation differential inequalities
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Quasilinear Robin Problem with Boundary Perturbation 认领 引用
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作者 CHEN Xue-dong 《Chinese Quarterly Journal of Mathematics》 北大核心 2006年第1期90-95,共6页
A class of quasilinear Robin problems with boundary perturbation are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the boundary value problem ... A class of quasilinear Robin problems with boundary perturbation are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the boundary value problem is studied. 展开更多
关键词 quasilinear Robin problem singular perturbation boundary perturbation
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Asymptotic expansions of finite element solutions to Robin problems in H^3 and their application in extrapolation cascadic multigrid method 认领 引用 被引量：1
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作者 HU HongLing CHEN ChuanMiao PAN KeJia 《Science China Mathematics》 SCIE 2014年第4期687-698,共12页
For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the... For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented. 展开更多
关键词 finite element Richardson extrapolation Robin problem asymptotic expansion cascadic multi-grid method
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Faber-Krahn Inequality for Robin Problems Involving p-Laplacian 认领 引用 被引量：1
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作者 Qiu-yi Dai Yu-xia Fu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2011年第1期13-28,共16页
The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed ... The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed volume, the ball has the smallest first eigenvalue. 展开更多
关键词 Robin problem p-Laplacian Faber-Krahn type inequality
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The spike layer solution to singular perturbation Robin boundary value problem for higher order elliptic equation 认领 引用
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作者 FENG Yi-hu HOU Lei 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2020年第4期410-416,共7页
The singularly perturbed Robin boundary value problem for the higher order elliptic equation is considered.Under suitable conditions,the existence and asymptotic behavior of solution to the boundary value problems are... The singularly perturbed Robin boundary value problem for the higher order elliptic equation is considered.Under suitable conditions,the existence and asymptotic behavior of solution to the boundary value problems are studied.The uniform validity of its asymptotic expansion is proved by using the fixed point theorem. 展开更多
关键词 nonlinear Robin problem spike layer
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A CLASS OF NONLINEAR PREDATOR-PREY SINGULARLY PERTURBED ROBIN PROBLEMS FOR REACTION DIFFUSION SYSTEM 认领 引用 被引量：1
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作者 Mo Jiaqi Zhang Weijiang +1 位作者 He Ming Yao Jingsun 《Annals of Differential Equations》 2006年第2期168-175,共8页
A class of nonlinear predator-prey singularly perturbed Robin problems for reaction diffusion systems are considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptot... A class of nonlinear predator-prey singularly perturbed Robin problems for reaction diffusion systems are considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of solution for the initial boundary value problems are studied. 展开更多
关键词 nonlinear predator-prey reaction diffusion singular perturbation Robin problem
THE CORNER LAYER SOLUTION TO ROBIN PROBLEM FOR REACTION DIFFUSION EQUATION 认领 引用
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作者 Lihua Chen Zhaohui Wen +1 位作者 Cheng Ouyang Jiaqi Mo 《Annals of Differential Equations》 2012年第2期132-136,共5页
A class of Robin boundary value problem for reaction diffusion equation is considered.Under suitable conditions,using the theory of differential inequalities the existence and asymptotic behavior of the corner layer s... A class of Robin boundary value problem for reaction diffusion equation is considered.Under suitable conditions,using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied. 展开更多
关键词 corner layer asymptotic solution Robin problem
The Nonlinear Predator-Prey Singularly Perturbed Robin Initial Boundary Value Problems for Reaction Diffusion System 认领 引用
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作者 莫嘉琪 《Journal of Shanghai Jiaotong university(Science)》 2003年第2期179-182,共4页
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence... The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied. 展开更多
关键词 nonlinear predator-prey reaction diffusion singular perturbation Robin problem
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浸入式虚拟元法求解Robin跳跃条件的椭圆界面问题 认领 引用
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作者 马俊驰 卢宣成 崔琳 《辽宁师范大学学报（自然科学版）》 CAS 2025年第3期359-366,共8页
应用浸入式虚拟元法求解带有Robin跳跃条件的椭圆界面问题.通过结合虚拟元法的几何灵活性和浸入式有限元法的界面处理能力,该方法在非匹配网格上构造协调的离散空间,并通过投影算子将虚拟元函数映射到满足界面跳跃条件的浸入式有限元空... 应用浸入式虚拟元法求解带有Robin跳跃条件的椭圆界面问题.通过结合虚拟元法的几何灵活性和浸入式有限元法的界面处理能力,该方法在非匹配网格上构造协调的离散空间,并通过投影算子将虚拟元函数映射到满足界面跳跃条件的浸入式有限元空间.本文考虑的Robin型跳跃条件,理论分析证明了该方法在L2范数和H1范数下收敛,通过数值实验验证了理论分析的准确性和可行性. 展开更多
关键词 浸入式虚拟元法 Robin跳跃条件 椭圆界面问题 非匹配网格
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Numerical Solutions to the Robin Inverse Problem with Nonnegativity Constraints 认领 引用
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作者 Weifu Fang Fu-Rong Lin 《Journal of Applied Mathematics and Physics》 2022年第6期2015-2025,共11页
We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary i... We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results. 展开更多
关键词 Robin Inverse Problem Ill-Posed Problem Laplace Equation Boundary Inte-gral Equation Nonnegativity Constraint Penalty Method
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改进Robin边界条件下抛物型方程控制系数反演 认领 引用
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作者 赵静 张永富 苏丽丽 《内蒙古民族大学学报（自然科学版）》 2025年第5期80-85,共6页
对改进Robin边界条件下含有控制系数的抛物型偏微分方程进行反演研究,并采用有限差分方法求解此问题。利用复化Simpson积分公式离散附加条件,并应用Crank-Nicolson差分法反演控制系数。通过数值算例显示,该方法对于此类抛物型方程控制... 对改进Robin边界条件下含有控制系数的抛物型偏微分方程进行反演研究,并采用有限差分方法求解此问题。利用复化Simpson积分公式离散附加条件,并应用Crank-Nicolson差分法反演控制系数。通过数值算例显示,该方法对于此类抛物型方程控制系数的反演是稳定有效的。 展开更多
关键词 抛物型方程反问题 改进Robin边界条件 Crank-Nicolson差分法 复化Simpson积分公式
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半线性方程ROBIN问题的角层解(英文) 认领 引用 被引量：21
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作者 莫嘉琪 陈怀军 《应用数学》 CSCD 北大核心 2012年第1期1-4,共4页
本文讨论了一类半线性方程Robin边值问题.利用微分不等式理论,研究了边值问题角层解的存在性和渐近性态.
关键词 角层 渐近解 Robin问题
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非线性种群反应扩散系统奇摄动ROBIN问题(英文) 认领 引用 被引量：4
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作者 莫嘉琪 姚静荪 王辉 《生物数学学报》 北大核心 2007年第2期193-199,共7页
研究了一类具有非线性种群反应扩散系统奇摄动Robin初始边值问题.在适当的条件下,利用微分不等式理论,讨论了问题解的存在性和渐近性态.
关键词 非线性 种群 反应扩散 奇摄动 Robin问题
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具有无穷大边界值的二阶拟线性奇摄动Robin问题的双边界层 认领 引用 被引量：2
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作者 周哲彦 沈建和 《福建师范大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第4期7-13,共7页
研究一类具有无穷大边界值的二阶拟线性奇摄动Robin边值问题的双边界层现象.基于边界层校正的思想,构造了左右端点附近的边界层函数(包括指数型与代数型),得到了该问题一致有效的渐近解;基于微分不等式理论,证明了该问题解的存在性,给... 研究一类具有无穷大边界值的二阶拟线性奇摄动Robin边值问题的双边界层现象.基于边界层校正的思想,构造了左右端点附近的边界层函数(包括指数型与代数型),得到了该问题一致有效的渐近解;基于微分不等式理论,证明了该问题解的存在性,给出了渐近解关于精确解的误差估计.一个典型的算例验证了所得结果的正确性. 展开更多
关键词 Robin问题 无穷大边界值 双边界层 边界层校正 微分不等式
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一类强非线性非自治方程的奇摄动Robin边值问题 认领 引用 被引量：2
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作者 石兰芳 莫嘉琪 《应用数学》 CSCD 北大核心 2017年第2期247-251,共5页
本文研究一类强非线性非自治方程的奇摄动Robin边值问题.利用奇异摄动的定性、稳定性理论和方法讨论两端边界值对解的渐近性态.并得到相应解具有边界层、内部层解的结果.
关键词 非线性 Robin问题 奇摄动
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具有多重解的非线性Robin问题的奇摄动(英文) 认领 引用 被引量：13
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作者 欧阳成 《应用数学》 北大核心 2002年第3期149-153,共5页
本文利用边界层法 ,研究了具有多重解的非线性Robin问题εx″+ f(t,x)x′+ g(t,x) =0 ,0 ≤t≤ 1 ,x′( 0 ,ε) -ax( 0 ,ε) =A ,x′( 1 ,ε) +bx( 1 ,ε) =B其中ε为正的小参数 .在适当的假设下 ,我们通过给出外部解展开式系数的一般... 本文利用边界层法 ,研究了具有多重解的非线性Robin问题εx″+ f(t,x)x′+ g(t,x) =0 ,0 ≤t≤ 1 ,x′( 0 ,ε) -ax( 0 ,ε) =A ,x′( 1 ,ε) +bx( 1 ,ε) =B其中ε为正的小参数 .在适当的假设下 ,我们通过给出外部解展开式系数的一般表达式 ,得到了退化问题的边值为某方程的多重根时的渐近解 ,推广了有关结果 . 展开更多
关键词 奇摄动 非线性 Robin问题 重根 渐近解
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非线性二阶Robin问题多正解的存在性 认领 引用 被引量：7
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作者 龙严 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2017年第2期249-252,共4页
本文利用不动点指数理论证明了如下非线性二阶Robin问题{u″(t)-k^2u(t)+λf(u(t))=0,t∈(0,1),k≠0,u'(0)=0,u(1)=0多个正解的存在性,其中f:[0,∞)→[0,∞)为连续函数且有多个零点,λ>0为参数.
关键词 Robin问题 多解性 不动点指数
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一类二次奇摄动Robin问题 认领 引用 被引量：5
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作者 葛志新 《工程数学学报》 CSCD 北大核心 2011年第2期245-250,共6页
本文研究了可描述某伴随有体积变化的化学反应的一类二次奇摄动边值问题.在适当的条件下,先利用幂级数形式展开法,就退化问题的边值条件的一重根、二重根、三重根分别构造了问题的外部解.其次利用伸长变量,构造问题的内层解,并应用微分... 本文研究了可描述某伴随有体积变化的化学反应的一类二次奇摄动边值问题.在适当的条件下,先利用幂级数形式展开法,就退化问题的边值条件的一重根、二重根、三重根分别构造了问题的外部解.其次利用伸长变量,构造问题的内层解,并应用微分不等式理论,证明了边值问题解的存在性、一致有效性和渐近性态. 展开更多
关键词 二次奇摄动 Robin问题 单根 二重根 三重根 微分不等式理论
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