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SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION
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作者 向长林 郑高峰 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期420-430,共11页
This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽... This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems. 展开更多
关键词 fourth order elliptic equation regularity theory Morrey space decay estimates Riesz potential
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Stokes'first problem for the fourth order fluid in a porous half space 被引量:4
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作者 T.Hayat F.Shahazad M.Ayub 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2007年第1期17-21,共5页
In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy's law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parame... In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy's law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parameters of interest on the velocity profile is revealed. 展开更多
关键词 fourth order fluid Porous space Numerical solution Modified Darcy's law
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MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE 被引量:3
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作者 许丽萍 陈海波 《Acta Mathematica Scientia》 SCIE CSCD 2015年第5期1067-1076,共10页
In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type {Δ^2u-(a+bfR^3|↓△u|^2dx)△u+V(x)u=f(x,u),x∈R^3, u∈H^2(R3),where a, b 〉 0 are constants and the primitive... In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type {Δ^2u-(a+bfR^3|↓△u|^2dx)△u+V(x)u=f(x,u),x∈R^3, u∈H^2(R3),where a, b 〉 0 are constants and the primitive of the nonlinearity f is of superlinear growth near infinity in u and is also allowed to be sign-changing. By using variational methods, we establish the existence and multiplicity of solutions. Our conditions weaken the Ambrosetti- Rabinowitz type condition. 展开更多
关键词 fourth order elliptic equations of Kirchhoff type symmetric mountain pass theorem variational methods
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The Energy-orthogonal Tetrahedral Finite Element for Fourth Order Elliptic Equations 被引量:1
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作者 LIU Ming-fang CAO Ji-wei CHEN Shao-chun 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第3期388-393,共6页
In this paper,the 16-parameter nonconforming tetrahedral element which has an energy-orthogonal shape function space is presented for the discretization of fourth order elliptic partial differential operators in three... In this paper,the 16-parameter nonconforming tetrahedral element which has an energy-orthogonal shape function space is presented for the discretization of fourth order elliptic partial differential operators in three spatial dimensions.The newly constructed element is proved to be convergent for a model biharmonic equation. 展开更多
关键词 nonconforming finite element tree-dimension fourth order elliptic equation
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Asymptotic behaviour of solution for fourth order wave equation with dispersive and dissipative terms
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作者 徐润章 赵希人 沈继红 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第2期259-262,共4页
This paper studies the initial boundary value problem of fourth order wave equation with dispersive and dissipative terms. By using multiplier method, it is proven that the global strong solution of the problem decays... This paper studies the initial boundary value problem of fourth order wave equation with dispersive and dissipative terms. By using multiplier method, it is proven that the global strong solution of the problem decays to zero exponentially as the time approaches infinite, under a very simple and mild assumption regarding the nonlinear term. 展开更多
关键词 fourth order wave equation DISPERSIVE DISSIPATIVE asymptotic behaviour
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BOUNDEDNESS AND UNIFORM BOUNDEDNESS RESULTS FOR CERTAIN NON-AUTONOMOUS DIFFERENTIAL EQUATIONS OF FOURTH ORDER
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作者 Cemil Tunc(西密尔·通兹) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第11期1273-1278,共6页
Sufficient conditions have been obtained so that all solutions of a different fourth order differential equation are bounded and uniformly bounded.
关键词 differential equation of fourth order Liapunov function BOUNDEDNESS uniform boundedness
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On the Oscillation of the Fourth Order Differential Equations
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作者 冯滨鲁 俞元洪 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第4期1-10, ,共10页
In the present paper sufficient conditions for oscillations and nonoscillations of a class of fourth order differential equations are obtained.
关键词 fourth order differential equations oscillatory solutions nonoscillatory solutions
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ADPTIVE INTERFERENCE CANCELER BASED ON FOURTH ORDER CUMULANT
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作者 MaYongfeng ZhangWeiqiang TaoRan 《Journal of Electronics(China)》 2005年第4期379-384,共6页
An adaptive interference cancler algorithm based on fourth-order cumulant is proposed to overcome the fault of conventional autocorrelation-based Least Mean Square (LMS)algorithm which cannot suppress the correlated G... An adaptive interference cancler algorithm based on fourth-order cumulant is proposed to overcome the fault of conventional autocorrelation-based Least Mean Square (LMS)algorithm which cannot suppress the correlated Gaussian noises. The recursive formulation of the proposed algorithm is given to reduce its computational complexity. The simulation results are presented to demonstrate the effectiveness of this novel approach. 展开更多
关键词 fourth order cumulant Noise canceler RECURSIVE
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A Maximum Principle Result for a General Fourth Order Semilinear Elliptic Equation
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作者 A. Mareno 《Journal of Applied Mathematics and Physics》 2016年第8期1682-1686,共5页
We obtain maximum principles for solutions of some general fourth order elliptic equations by modifying an auxiliary function introduced by L.E. Payne. We give a brief application of these maximum principles by deduci... We obtain maximum principles for solutions of some general fourth order elliptic equations by modifying an auxiliary function introduced by L.E. Payne. We give a brief application of these maximum principles by deducing apriori bounds on a certain quantity of interest. 展开更多
关键词 NONLINEAR fourth order Partial Differential Equation SEMILINEAR
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POSITIVE SOLUTIONS OF A FOURTH ORDER BOUNDARY VALUE PROBLEM 被引量:3
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作者 Ren LishunDept. of Math., Zhoukou Teachers College, Henan 466000,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第2期138-142,共5页
The existence of positive solutions of the nonlinear fourth order problemu (4)(x)=λa(x)f(u(x)), u(0)=u′(0)=u′(1)=u(1)=0is studied, where a:[0,1]→R may change sign, f(0)>0,λ>0 is sufficiently small. Our ... The existence of positive solutions of the nonlinear fourth order problemu (4)(x)=λa(x)f(u(x)), u(0)=u′(0)=u′(1)=u(1)=0is studied, where a:[0,1]→R may change sign, f(0)>0,λ>0 is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem. 展开更多
关键词 fourth-order boundary value problem positive solution Leray-Schauder fixed point theorem.
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Existence of positive solutions for fourth order singular differential equations with Sturm-Liouville boundary conditions 被引量:1
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作者 Zhao Zengqin 《商丘师范学院学报》 CAS 2007年第12期1-8,共8页
By using the upper and lower solutions method and fixed point theory,we investigate a class of fourth-order singular differential equations with the Sturm-Liouville Boundary conditions.Some sufficient conditions are o... By using the upper and lower solutions method and fixed point theory,we investigate a class of fourth-order singular differential equations with the Sturm-Liouville Boundary conditions.Some sufficient conditions are obtained for the existence of C2[0,1] positive solutions and C3[0,1] positive solutions. 展开更多
关键词 存在性 四阶微分方程 减函数 Sturm-Liouville边值 正解
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Existence of Multiple Positive Solutions for Fourth Order Two-point Boundary Value Problems 被引量:1
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作者 戚仕硕 《Northeastern Mathematical Journal》 CSCD 2002年第1期63-72,共10页
The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples ... The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples are given to show the validity of these results. 展开更多
关键词 existence theorem multiple positive solution fourth-order boundary value problem
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The Basic (<i>G'/G</i>)-Expansion Method for the Fourth Order Boussinesq Equation
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作者 Hasibun Naher Farah Aini Abdullah 《Applied Mathematics》 2012年第10期1144-1152,共9页
The (G'/G)-expansion method is simple and powerful mathematical tool for constructing traveling wave solutions of nonlinear evolution equations which arise in engineering sciences, mathematical physics and real ti... The (G'/G)-expansion method is simple and powerful mathematical tool for constructing traveling wave solutions of nonlinear evolution equations which arise in engineering sciences, mathematical physics and real time application fields. In this article, we have obtained exact traveling wave solutions of the nonlinear partial differential equation, namely, the fourth order Boussinesq equation involving parameters via the (G'/G)-expansion method. In this method, the general solution of the second order linear ordinary differential equation with constant coefficients is implemented. Further, the solitons and periodic solutions are described through three different families. In addition, some of obtained solutions are described in the figures with the aid of commercial software Maple. 展开更多
关键词 The (G'/G)-Expansion Method the fourth order BOUSSINESQ Equation TRAVELING Wave Solutions Nonlinear Partial Differntial Equations
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An Adaptive Least-Squares Mixed Finite Element Method for Fourth Order Parabolic Problems
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作者 Ning Chen Haiming Gu 《Applied Mathematics》 2013年第4期675-679,共5页
A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approxi... A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved. 展开更多
关键词 ADAPTIVE METHOD LEAST-SQUARES Mixed Finite Element METHOD fourth order Parabolic Problems LEAST-SQUARES Functional A POSTERIORI Error
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New Fourth Order Iterative Methods Second Derivative Free
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作者 Osama Y. Ababneh 《Journal of Applied Mathematics and Physics》 2016年第3期519-523,共5页
In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574... In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574], suggested a fourth-order method for solving nonlinear equations. Per iteration in this method requires two evaluations of the function and two of its first derivatives;therefore, the efficiency index is 1.41421 as Newton’s method. In this paper, we modified this method and obtained a family of iterative methods for appropriate and suitable choice of the parameter. It should be noted that per iteration for the new methods requires two evaluations of the function and one evaluation of its first derivatives, so its efficiency index equals to 1.5874. Analysis of convergence shows that the methods are fourth-order. Several numerical examples are given to illustrate the performance of the presented methods. 展开更多
关键词 Newton’s Method fourth-order Convergence Third-order Convergence Non-Linear Equations ROOT-FINDING Iterative Method
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A New Fourth Order Difference Approximation for the Solution of Three-dimensional Non-linear Biharmonic Equations Using Coupled Approach
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作者 Ranjan Kumar Mohanty Mahinder Kumar Jain Biranchi Narayan Mishra 《American Journal of Computational Mathematics》 2011年第4期318-327,共10页
This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equations. At each inter... This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equations. At each internal grid point, the solution u(x,y,z) and its Laplacian Δ4u are obtained. The resulting stencil algo-rithm is presented and hence this new algorithm can be easily incorporated to solve many problems. The present discretization allows us to use the Dirichlet boundary conditions only and there is no need to discretize the derivative boundary conditions near the boundary. We also show that special treatment is required to handle the boundary conditions. Convergence analysis for a model problem is briefly discussed. The method is tested on three problems and compares very favourably with the corresponding second order approximation which we also discuss using coupled approach. 展开更多
关键词 THREE-DIMENSIONAL NON-LINEAR BIHARMONIC Equation Finite Differences fourth order Accuracy Compact Discretization Block-Block-Tridiagonal Tangential Derivatives Laplacian Stream Function REYNOLDS Number
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Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function
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作者 Junrui Yue Yun Zhang Qingyue Bai 《Open Journal of Applied Sciences》 2024年第1期63-69,共7页
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a... This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique. 展开更多
关键词 fourth-order Three-Point Boundary Value Problem Sign-Changing Green’s Function Fixed Point Index Iterative Technique Monotone Positive Solution EXISTENCE
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Fourth-Order Predictive Modelling: II. 4th-BERRU-PM Methodology for Combining Measurements with Computations to Obtain Best-Estimate Results with Reduced Uncertainties
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作者 Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2023年第4期439-475,共37页
This work presents a comprehensive fourth-order predictive modeling (PM) methodology that uses the MaxEnt principle to incorporate fourth-order moments (means, covariances, skewness, kurtosis) of model parameters, com... This work presents a comprehensive fourth-order predictive modeling (PM) methodology that uses the MaxEnt principle to incorporate fourth-order moments (means, covariances, skewness, kurtosis) of model parameters, computed and measured model responses, as well as fourth (and higher) order sensitivities of computed model responses to model parameters. This new methodology is designated by the acronym 4<sup>th</sup>-BERRU-PM, which stands for “fourth-order best-estimate results with reduced uncertainties.” The results predicted by the 4<sup>th</sup>-BERRU-PM incorporates, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2<sup>nd</sup>-BERRU-PM, and vastly generalizes the results produced by extant data assimilation and data adjustment procedures. 展开更多
关键词 fourth-order Predictive Modeling Data Assimilation Data Adjustment Uncertainty Quantification Reduced Predicted Uncertainties
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Fourth-Order Predictive Modelling: I. General-Purpose Closed-Form Fourth-Order Moments-Constrained MaxEnt Distribution
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作者 Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2023年第4期413-438,共26页
This work (in two parts) will present a novel predictive modeling methodology aimed at obtaining “best-estimate results with reduced uncertainties” for the first four moments (mean values, covariance, skewness and k... This work (in two parts) will present a novel predictive modeling methodology aimed at obtaining “best-estimate results with reduced uncertainties” for the first four moments (mean values, covariance, skewness and kurtosis) of the optimally predicted distribution of model results and calibrated model parameters, by combining fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters. Underlying the construction of this fourth-order predictive modeling methodology is the “maximum entropy principle” which is initially used to obtain a novel closed-form expression of the (moments-constrained) fourth-order Maximum Entropy (MaxEnt) probability distribution constructed from the first four moments (means, covariances, skewness, kurtosis), which are assumed to be known, of an otherwise unknown distribution of a high-dimensional multivariate uncertain quantity of interest. This fourth-order MaxEnt distribution provides optimal compatibility of the available information while simultaneously ensuring minimal spurious information content, yielding an estimate of a probability density with the highest uncertainty among all densities satisfying the known moment constraints. Since this novel generic fourth-order MaxEnt distribution is of interest in its own right for applications in addition to predictive modeling, its construction is presented separately, in this first part of a two-part work. The fourth-order predictive modeling methodology that will be constructed by particularizing this generic fourth-order MaxEnt distribution will be presented in the accompanying work (Part-2). 展开更多
关键词 Maximum Entropy Principle fourth-order Predictive Modeling Data Assimilation Data Adjustment Reduced Predicted Uncertainties Model Parameter Calibration
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OSCILLATIONS OF FOURTH ORDER ODE WITH IMPULSES 被引量:13
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作者 冯伟贞 《Annals of Differential Equations》 2003年第2期136-145,共10页
Sufficient conditions to guarantee the oscillations of fourth order ODE with impulses are obtained. The importance of the impulsive effect on the oscillations of higher order differential equations is stressed.
关键词 fourth order ODE with impulses solution of fourth order ODE with impulses OSCILLATION
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