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RIEMANN BOUNDARY VALUE PROBLEMS FOR SOME K-REGULAR FUNCTIONS IN CLIFFORD ANALYSIS 被引量:3
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作者 姜乐 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2012年第5期2029-2049,共21页
In this paper,we study the R m(m〉0) Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C(Vn,n).By using Plemelj formula,... In this paper,we study the R m(m〉0) Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C(Vn,n).By using Plemelj formula,we get the solutions of R m(m〉0) Riemann boundary value problems for regular functions.Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions,we obtain the solutions of R m(m〉0) Riemann boundary value problems for harmonic functions and bi-harmonic functions. 展开更多
关键词 Riemann boundary value problem harmonic function bi-harmonic function Plemelj formula
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THE EXISTENCE AND STABILITY OF NORMALIZED SOLUTIONS FOR A BI-HARMONIC NONLINEAR SCHR?DINGER EQUATION WITH MIXED DISPERSION
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作者 罗庭健 郑世骏 朱世辉 《Acta Mathematica Scientia》 SCIE CSCD 2023年第2期539-563,共25页
In this paper,we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrodinger equation with aμ-Laplacian term(BNLS).Such BNLS models the propagation of intense laser beams in a bu... In this paper,we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrodinger equation with aμ-Laplacian term(BNLS).Such BNLS models the propagation of intense laser beams in a bulk medium with a second-order dispersion term.Denoting by Qpthe ground state for the BNLS withμ=0,we prove that in the mass-subcritical regime p∈(1,1+8/d),there exist orbit ally stable ground state solutions for the BNLS when p∈(-λ0,∞)for someλ0=λ0(p,d,‖Qp‖L2)>0.Moreover,in the mass-critical case p=1+8/d,we prove the orbital stability on a certain mass level below‖Q*‖L2,provided thatμ∈(-λ1,0),where■and Q*=Q1+8/d.The proofs are mainly based on the profile decomposition and a sharp Gagliardo-Nirenberg type inequality.Our treatment allows us to fill the gap concerning the existence of the ground states for the BNLS when p is negative and p∈(1,1+8/d]. 展开更多
关键词 elliptic equations bi-harmonic operator normalized solutions profile decomposition
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UNIQUENESS FOR THE SOLUTIONS OF ELASTIC THIN PLATES AND SHALLOW SHELLS AS WELL AS THEIR CONTACT PROBLEM WITH HALF SPACE
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作者 范家参 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第3期335-340,共6页
The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the sec... The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the second. 展开更多
关键词 harmonic and bi-harmonic functions uniqueness of solution elastic plates and shallow shells contact problem with the elastic half space
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GLOBAL L^p ESTIMATES FOR THE PARABOLIC EQUATION OF THE BI-HARMONIC TYPE 被引量:2
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作者 Yao Fengping Zhou Shulin 《Journal of Partial Differential Equations》 2008年第4期315-334,共20页
In this paper similarly to the second-order case, we give an elementary and straightforward proof of global Lp estimates for the initial-value parabolic problem of the bi-harmonic type. Moreover, we obtain the existen... In this paper similarly to the second-order case, we give an elementary and straightforward proof of global Lp estimates for the initial-value parabolic problem of the bi-harmonic type. Moreover, we obtain the existence and uniqueness of the solutions in the suitable space using the potential theory, Marcinkiewicz interpolation theorem and approximation argument. Meanwhile, by the same approach we can deal with the general polyharmonic cases. 展开更多
关键词 bi-harmonic PARABOLIC Lp estimates existence uniqueness.
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THE EXISTENCE AND NON-EXISTENCE OF SIGN-CHANGING SOLUTIONS TO BI-HARMONIC EQUATIONS WITH A p-LAPLACIAN 被引量:1
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作者 Wenqing WANG Anmin MAO 《Acta Mathematica Scientia》 SCIE CSCD 2022年第2期551-560,共10页
We investigate the bi-harmonic problem{Δ^(2)u-α▽·(f(▽u))-βΔ_(p)u=g(x,u) in Ω,δu/δn=0,δ(Δu)/δn=0 on δΩ,where Δ^(2)u=Δ(Δu),Δ_(p)u=div(|▽u|^(p-2)▽u)with p>2.Ω is a bounded smooth domain in R^... We investigate the bi-harmonic problem{Δ^(2)u-α▽·(f(▽u))-βΔ_(p)u=g(x,u) in Ω,δu/δn=0,δ(Δu)/δn=0 on δΩ,where Δ^(2)u=Δ(Δu),Δ_(p)u=div(|▽u|^(p-2)▽u)with p>2.Ω is a bounded smooth domain in R^(N),N≥1.By using a special function space with the constraint ∫_(Ω)udx=0,under suitable assumptions on f and g(x,u),we show the existence and multiplicity of sign-changing solutions to the above problem via the Mountain pass theorem and the Fountain theorem.Recent results from the literature are extended. 展开更多
关键词 bi-harmonic sign-changing solution Fountain theorem
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双调和型抛物方程的Schauder估计 被引量:2
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作者 姚锋平 周蜀林 《应用数学和力学》 CSCD 北大核心 2007年第11期1340-1352,共13页
该文给出了双调和型抛物方程初值问题解的Schauder估计,并且在适当的空间中证明了解的存在性与惟一性.类似于二阶情形,首先通过Fourier变换得到一个形式解,然后再利用位势理论和逼近方法得到解的正则性、唯一性及存在性.该方法简单而易懂.
关键词 双调和 抛物 SCHAUDER估计 存在性 惟一性
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BOUNDARY INTEGRAL FORMULAS FOR ELASTIC PLANE PROBLEM OF EXTERIOR CIRCULAR DOMAIN
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作者 董正筑 李顺才 余德浩 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第7期993-1000,共8页
After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress func... After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain. 展开更多
关键词 elastic plane problem of exterior circular domain bi-harmonic equation Fourier series stress function boundary integral formula
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BOUNDARY INTEGRAL FORMULA OF ELASTICPROBLEMS IN CIRCLE PLANE
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作者 董正筑 李顺才 余德浩 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第5期604-608,共5页
By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be dire... By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which does not include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient. 展开更多
关键词 elastic problem in circle plane bi-harmonic equation stress function boundary integral formula
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Schauder estimates for parabolic equation of bi-harmonic type
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作者 姚锋平 周蜀林 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第11期1503-1516,共14页
Global Schauder estimates for the initial-value parabolic problem of the hi-harmonic type are proved, and the existence and uniqueness of the solutions in the suitable space are obtained. Similarly to the second-order... Global Schauder estimates for the initial-value parabolic problem of the hi-harmonic type are proved, and the existence and uniqueness of the solutions in the suitable space are obtained. Similarly to the second-order case, first a formal expression of solutions by the Fourier transform is obtained, and then the regularity, uniqueness and existence of solutions using the potential theory and approximation argument are got. out approach is simple and straightforward. 展开更多
关键词 bi-harmonic PARABOLIC Schauder estimates EXISTENCE UNIQUENESS
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Analytical solutions for a uniformly loaded circular plate with clamped edges
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作者 丁皓江 李翔宇 陈伟球 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第10期1163-1168,共6页
A bi-harmonic potential function was constructed in this study. Love solution was employed to obtain analytical solutions of uniformly loaded plates with two different types of clamped edges. The treatment of clamped ... A bi-harmonic potential function was constructed in this study. Love solution was employed to obtain analytical solutions of uniformly loaded plates with two different types of clamped edges. The treatment of clamped boundary conditions was the same as that adopted by Timoshenko and Goodier (1970). The analytical solution for the first type of clamped boundary condition is identical with that obtained by Luo et al.(2004), and the solutions for both types were compared with the FEM results and the calculations of thin plate theory. 展开更多
关键词 Three-dimensional analytical solution Circular plates with clamped edges bi-harmonic functions Axisymmetricdeformation
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半平面体弹性问题的边界积分公式及应用 被引量:18
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作者 彭维红 董正筑 李顺才 《中国矿业大学学报》 EI CAS CSCD 北大核心 2005年第3期400-404,共5页
从格林函数和双调和函数的基本解出发,将双调和方程的边值问题转化为一个只与边界面力有关的边界积分方程,进而求得具体面力条件下半平面弹性问题的解析解.并用以研究底板岩层中的应力分布,得到了底板应力增量分布的解析计算公式,该公... 从格林函数和双调和函数的基本解出发,将双调和方程的边值问题转化为一个只与边界面力有关的边界积分方程,进而求得具体面力条件下半平面弹性问题的解析解.并用以研究底板岩层中的应力分布,得到了底板应力增量分布的解析计算公式,该公式直观、简洁,便于进行数值计算. 展开更多
关键词 积分公式 平面体 应用 边界积分方程 平面弹性问题 解析计算公式 双调和函数 双调和方程 格林函数 问题转化 应力分布 底板岩层 应力增量 数值计算 基本解 界面力 解析解 边值
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求解含有高阶导数偏微分方程的局部间断Petrov-Galerkin方法(英文) 被引量:6
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作者 赵国忠 蔚喜军 +1 位作者 郭虹平 董自明 《计算物理》 EI CSCD 北大核心 2019年第5期517-532,共16页
构造一类求解三种类型偏微分方程的间断Petrov-Galerkin方法.求解的方程分别含有二阶、三阶和四阶偏导数,包括Burgers型方程、KdV型方程和双调和型方程.首先将高阶微分方程转化成为与之等价的一阶微分方程组,再将求解双曲守恒律的间断Pe... 构造一类求解三种类型偏微分方程的间断Petrov-Galerkin方法.求解的方程分别含有二阶、三阶和四阶偏导数,包括Burgers型方程、KdV型方程和双调和型方程.首先将高阶微分方程转化成为与之等价的一阶微分方程组,再将求解双曲守恒律的间断Petrov-Galerkin方法用于求解微分方程组.该方法具有四阶精度且具有间断Petrov-Galerkin方法的优点.数值实验表明该方法可以达到最优收敛阶而且可以模拟复杂波形相互作用,如孤立子的传播及相互碰撞等. 展开更多
关键词 KDV型方程 双调和方程 局部间断Petrov-Galerkin方法 孤立子演化
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圆外平面弹性问题的边界积分公式 被引量:4
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作者 董正筑 李顺才 余德浩 《应用数学和力学》 CSCD 北大核心 2006年第7期867-873,共7页
将边界上的应力函数及其法向导数展开为罗朗级数,与复应力函数的罗朗级数的表达式对比,可以确定罗朗级数的各系数,再利用傅利叶级数和卷积的几个公式进行计算,得到应力函数边界积分公式.通过边界的应力函数及其法向导数的积分,直接得到... 将边界上的应力函数及其法向导数展开为罗朗级数,与复应力函数的罗朗级数的表达式对比,可以确定罗朗级数的各系数,再利用傅利叶级数和卷积的几个公式进行计算,得到应力函数边界积分公式.通过边界的应力函数及其法向导数的积分,直接得到圆外应力函数值,并给出几个算例,表明结果用于求解单位圆外平面弹性问题十分方便. 展开更多
关键词 圆外平面弹性问题 双调和方程 傅利叶级数 应力函数 边界积分公式
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含Hardy位势的双调和方程特征值问题 被引量:5
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作者 伍芸 姚仰新 柯敏 《山东大学学报(理学版)》 CAS CSCD 北大核心 2008年第9期81-84,共4页
对于一类包含Hardy位势1/|x|4(N≥5)的双调和方程的特征值问题,通过建立一个新空间和一个Hardy-Rellich不等式证明该特征值问题的解的存在性。
关键词 特征值问题 双调和方程 HARDY位势
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Bi-f-harmonic map equations on singly warped product manifolds
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作者 ZHAO Chun-li LU Wei-jun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第1期111-126,共16页
Bi-f-harmonic maps are the critical points of bi-f-energy functional. This class of maps tends to integrate bi-harmonic maps and f-harmonic maps. In this paper, we show that bi-f-harmonic maps are not only an extensio... Bi-f-harmonic maps are the critical points of bi-f-energy functional. This class of maps tends to integrate bi-harmonic maps and f-harmonic maps. In this paper, we show that bi-f-harmonic maps are not only an extension of f-harmonic maps but also an extension of bi-harmonic maps, and that there should exist many examples of proper bi-f-harmonic maps. In order to find some concrete examples of proper bi-f-harmonic maps, we study the basic properties of bi-f-harmonic maps from two directions which are conformal maps between the same dimensionM manifolds and some special maps from or into a warped product manifold. 展开更多
关键词 f-tension field bi-f-tension field bi-f-harmonic map f-bi-harmonic map singly warped productmanifold.
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圆内平面弹性问题的边界积分公式 被引量:4
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作者 董正筑 李顺才 余德浩 《应用数学和力学》 CSCD 北大核心 2005年第5期556-560,共5页
 根据双解析函数可以得到单位圆内平面弹性问题应力函数的边界积分公式,但式中包含强奇异积分,不能用于直接计算· 将边界上的应力函数展开为Fourier级数,再利用广义函数论中的几个公式进行卷积计算,可以得到不含强奇异积分核的...  根据双解析函数可以得到单位圆内平面弹性问题应力函数的边界积分公式,但式中包含强奇异积分,不能用于直接计算· 将边界上的应力函数展开为Fourier级数,再利用广义函数论中的几个公式进行卷积计算,可以得到不含强奇异积分核的边界积分公式,通过边界的应力函数值和法向导数的积分,直接得到圆内应力函数值,并给出几个算例。 展开更多
关键词 圆内平面 弹性问题 双调和方程 应力函数 边界积分公式
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On f-bi-harmonic maps and bi-f-harmonic maps between Riemannian manifolds
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作者 LU WeiJun 《Science China Mathematics》 SCIE CSCD 2015年第7期1483-1498,共16页
Both bi-harmonic maps and f-harmonic maps have some nice physical motivation and applications.Motivated largely by f-tension field not involving Riemannian curvature tensor, we attempt to formalize some large objects ... Both bi-harmonic maps and f-harmonic maps have some nice physical motivation and applications.Motivated largely by f-tension field not involving Riemannian curvature tensor, we attempt to formalize some large objects so as to broaden the notions of f-tension field and bi-tension field. We introduce a very large generalization of harmonic maps called f-bi-harmonic maps as the critical points of f-bi-energy functional, and then derive the Euler-Lagrange equation of f-bi-energy functional given by the vanishing of f-bi-tension field.Subsequently, we study some properties of f-bi-harmonic maps between the same dimensional manifolds and give a non-trivial example. Furthermore, we also study the basic properties of f-bi-harmonic maps on a warped product manifold so that we could find some interesting and complicated examples. 展开更多
关键词 bi-f-tension field f-bi-tension field bi-f-harmonic map f-bi-harmonic map singly warped prod-uct manifold
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矩形边界平面问题在边界条件作用下应力解 被引量:1
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作者 许琪楼 《郑州大学学报(工学版)》 CAS 北大核心 2011年第5期1-6,共6页
边界条件作用下平面问题应力解为双调和方程解,由通解和特解组成.应力函数通解为含有8个待定系数的双向单三角级数,与矩形边界8个边界条件相对应;级数曲线波形符合相应方向边界法向面力或法向位移固有分布特点.应力函数特解有边界法向... 边界条件作用下平面问题应力解为双调和方程解,由通解和特解组成.应力函数通解为含有8个待定系数的双向单三角级数,与矩形边界8个边界条件相对应;级数曲线波形符合相应方向边界法向面力或法向位移固有分布特点.应力函数特解有边界法向面力、边界法向位移和边界常量剪应力3种;将任意分布的边界法向面力和边界法向位移进行格式化处理,由给定构造规则确定前2个特解.在特定边界条件下常量剪应力特解可不予考虑.随法向边界条件的变化有16种应力函数表达式,以处理256种矩形边界平面问题,推导了常见边界的特解表达式,分析了求解过程中的几个问题,并附有算例. 展开更多
关键词 弹性力学 平面问题 双调和方程 应力函数通解 应力函数特解
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基于不等齿靴的双谐波永磁电机优化设计 被引量:1
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作者 童涛 童超 李唐兵 《微电机》 2021年第2期19-24,共6页
五相永磁同步电机可利用双谐波(基波和三次谐波)电流输出转矩,因此需同时考虑基波和三次谐波绕组因数及磁动势谐波含量;分数槽集中绕组的绕组因数小于1,且磁动势谐波含量丰富;针对该问题,提出采用电枢齿与辅助齿齿靴弧度不等的五相双谐... 五相永磁同步电机可利用双谐波(基波和三次谐波)电流输出转矩,因此需同时考虑基波和三次谐波绕组因数及磁动势谐波含量;分数槽集中绕组的绕组因数小于1,且磁动势谐波含量丰富;针对该问题,提出采用电枢齿与辅助齿齿靴弧度不等的五相双谐波电机,根据解析推导出不等齿靴对双谐波电机绕组因数和磁动势谐波分布影响的数学模型。建立等齿靴与不等齿靴有限元模型对比仿真,验证了不等齿靴的双谐波永磁同步电机比等齿靴有更高的空载反电动势基波、三次谐波含量和更低的七次、九次谐波含量;在相同电流密度下,基于不等弧度齿靴的双谐波电机输出转矩性能更好。 展开更多
关键词 齿靴弧度 双谐波电机 绕组因数 磁动势 转矩脉动
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三分谢尔宾斯基垫片上的调和函数与双调和函数的算法
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作者 王丽 《江苏理工学院学报》 2014年第4期59-63,共5页
在这篇文章中,我们首先介绍了三分谢尔宾斯基垫片和标准拉普拉斯算子;其次,我们推导出了三分谢尔宾斯基垫片上调和函数与双调和函数的算法。图的顶点上这些函数的算法最后得出了预垫片,也就是近似三分谢尔宾斯基垫片。
关键词 算法 标准拉普拉斯算子 调和函数 双调和函数
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