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Complex variable solution for boundary value problem with X-shaped cavity in plane elasticity and its application*

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Applied Mathematics and Mechanics(English Edition) 2017年第9期38卷 1329-1346页

作者： Hang ZHOU College of Civil Engineering Key Laboratory of New Technology for Construction of Cities in Mountain AreaChongqing UniversityChongqing 400045China State Key Laboratory for Geomechanics and Deep Underground Engineering China University of Mining and TechnologyXuzhou 221116Jiangsu ProvinceChina

A new type of displacement pile, the X-section cast-in-place concrete （XCC） pile, has recently been developed in China. Extensive field tests and laboratory experi- ments are undertaken to evaluate its performance and quantify the non-uniform deforma- tion effect （NUDE） of the X-shaped cross section during installation. This paper develops a simplified theoretical model that attempts to capture the NUDE. Based on the theory of complex variable plane elasticity, closed-form solutions of the stress and displacement for the X-shaped cavity boundary value problem are given. Subsequently, the analytical solution is used to evaluate the NUDE, the concrete filling index （CFI）, and the perimeter reduction coefficient of the XCC pile cross section. The computed results are compared with field test results, showing reasonable agreement. The present simplified theoretical model reveals the deformation mechanism of the X-shaped cavity and facilitates applica- tion of the newly developed XCC pile technique in geotechnical engineering.

关键词： complex variable solution boundary value problem plane elasticity X-section cast-in-place concrete (XCC) pile deformation mechanism theoretical study

On Mixed Pressure-Velocity Regularity Criteria to the Navier-stokes Equations in Lorentz Spaces,Part Ⅱ:The Non-slip boundary value problem

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Chinese Annals of Mathematics,Series B 2022年第1期43卷 51-58页

作者： Hugo BEIRÃO DA VEIGA Jiaqi YANG Department of Mathematics Pisa UniversityPisaItaly School of Mathematics and Statistics Northwestern Polytechnical UniversityXi'an 710129China

This paper is a continuation of the authors recent work[Beirao da Veiga,*** Yang,J.,On mixed pressure-velocity regularity criteria to the Navier-Stokes equations in Lorentz spaces,***.,42(1),2021,1-16],in which mixed pressure-velocity criteria in Lorentz spaces for Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations,in the whole space R^(3) and in the periodic torus T^(3),are *** purpose of the present work is to extend the result of mentioned above to smooth,bounded domains Ω,under the non-slip boundary *** π denote the fluid pressure and v the fluid *** is shown that if π/(1+|v|^(θ))∈L^(p)(0,T;L^(q,∞)(Ω)),where 0≤θ≤1,and 2/p+3/q=2-θwith p≥2,then v is regular on Ω×(0,T].

关键词： Navier-Stokes equations Pressure-speed links Regularity criteria Lorentz spaces boundary value problem

FRACTIONAL ORDER boundary value problem WITH INTEGRAL boundary CONDITIONS INVOLVING PETTIS INTEGRAL

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Acta Mathematica Scientia 2011年第2期31卷 661-672页

作者： Hussein A.H. Salem Department of Mathematics Faculty of Sciences Alexandria University Department of Mathematics Faculty of Sciences and Arts Taibah University

In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.

关键词： Fractional calculus Pseudo solution boundary value problem Pettis integrals

ON A boundary value problem FOR A STURM-LIOUVILLE TYPE DIFFERENTIAL INCLUSION

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Journal of Systems Science & Complexity 2010年第2期23卷 390-394页

作者： Aurelian CERNEA Faculty of Mathematics and Informatics University of Bucharest

This paper proves a Filippov type existence theorem for solutions of a boundary valueproblem for a Sturm-Liouville type differential inclusion defined by a nonconvex set-valued *** consists in application of the contr... 详细信息

关键词： boundary value problem contractive set-valued map fixed point.

Multiplicity of Positive Solutions to M-point boundary value problem of Second Order Impulsive Differential Equations

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Acta Mathematicae Applicatae Sinica 2010年第1期26卷 145-158页

作者： Yuan-sheng Tian Chun-gen Liu Department of Mathematics Xiangnan University Chenzhou 423000 China School of Mathematics and LPMC Nankai University Tianjin 300071 China

In this paper, by using Avery-Peterson theorem on a convex cone, we consider the m-point boundary value problems for second order impulsive differential equations with the nonlinear term depending on the first order d... 详细信息

关键词： boundary value problem impulsive differential equations fixed-point theorem positive solutions

EXISTENCE OF SOLUTIONS FOR HIGHER ORDER MULTI-POINT boundary value problem AT RESONANCE

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Applied Mathematics and Mechanics(English Edition) 2006年第5期27卷 705-711页

作者：林晓洁杜增吉葛渭高 Department of Mathematics Xuzhou Normal UniversityXuzhouJiangsu 221116P.R. China Department of Mathematics Beijing Institute of TechnologyBeijing 100081P.R. China

Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new... 详细信息

关键词： boundary value problem resonance coincidence degree theory

Generalized variational principles for boundary value problem of electromagnetic field in electrodynamics

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Applied Mathematics and Mechanics(English Edition) 2010年第4期31卷 471-480页

作者：刘彬王作君郑世科 Key Laboratory of Measurement Technology and Instrumentation of Hebei Province Yanshan University Qinhuangdao 066004 Hebei Province P. R. China

An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien＇s method, a pair of generalized variational principles （GVPs） are established, which directly leads to all four Maxwell＇s equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem.

关键词： generalized variational principle (GVP) electromagnetic field electrodynamics boundary value problem finite element method

ON SOLVABILITY OF A boundary value problem FOR THE POISSON EQUATION WITH A NONLOCAL boundary OPERATOR

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Acta Mathematica Scientia 2015年第5期35卷 970-980页

作者： B.J.KADIRKULOV M.KIRANE Tashkent State Institute for Oriental Studies Laboratoire de Mathématiques Image et Applications Université de La Rochelle NAAM Research Group Department of Mathematics Faculty of ScienceKing Abdulaziz University

In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.

关键词： operator of fractional integration and differentiation solvability boundary value problem Riemann-Liouville operator Caputo fractional derivative Poisson equation Dirichlet and Neumann problems

SINGULAR PERTURBATION OF boundary value problem FOR QUASILINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

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Applied Mathematics and Mechanics(English Edition) 2001年第2期22卷 229-236页

作者：林苏榕田根宝林宗池 Mathernatical Section Fujian Broadcasting TV University Fuzhou 350003 P R China Department of Mathematics S hanghai Railroad University S hanghai 200333 P R China Department of Mathernatics Fujian Normal University Fuzhou 350007 P R China

The singularly perturbed boundary value problem for quasilinear third-order ordinary differential equation involving two small parameters has been considered. For the three cases epsilon/mu (2) --> 0(mu --> 0), mu (2)/epsilon --> 0(epsilon --> 0) and epsilon = mu (2), the formal asymptotic solutions are constructed by the method of two steps expansions and the existences of solution are proved by using the differential inequality method. In addition, the uniformly valid estimations of the remainder term are given as well.

关键词： two-parameters singular perturbation boundary value problem asymptotic expansion