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ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS
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作者 Jun CHEN Xuemei DENG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1903-1915,共13页
We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across th... We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners. 展开更多
关键词 elliptic equations divergence form discontinuous coefficients corner regularity
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The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles
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作者 Mingyu Wu 《Journal of Applied Mathematics and Physics》 2024年第4期1043-1049,共7页
This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of suff... This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order. 展开更多
关键词 Mixed Boundary Value Problems for elliptic equations Small-Angle Boundary Value Problems Regularity of Solutions to elliptic equations
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Besov Estimates for Sub-Elliptic Equations in the Heisenberg Group
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作者 Huimin Cheng Feng Zhou 《Advances in Pure Mathematics》 2024年第9期744-758,共15页
In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Be... In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderón-Zygmund theory in the Heisenberg group. 展开更多
关键词 Heisenberg Group Sub-elliptic equations REGULARITY Besov Spaces
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Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the(2+1)-dimensional elliptic Toda equation
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作者 庞福忠 葛根哈斯 赵雪梅 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第5期200-217,共18页
The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions ... The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations. 展开更多
关键词 (2+1)-dimensional elliptic Toda equation resonant interaction lump molecules
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A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations
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作者 Yiming Wen Luoping Chen Jiajia Dai 《Journal of Applied Mathematics and Physics》 2023年第2期361-376,共16页
In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the m... In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator. 展开更多
关键词 Two-Grid Mixed Finite Element Methods Posteriori Error Estimates Semilinear elliptic equations Averaging Technique
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Entropy Formulation for Triply Nonlinear Degenerate Elliptic-Parabolic-Hyperbolic Equation with Zero-Flux Boundary Condition
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作者 Mohamed Karimou Gazibo 《Journal of Applied Mathematics and Physics》 2023年第4期933-948,共16页
In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate pa... In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition. 展开更多
关键词 Degenerate elliptic-Parabolic Hyerbolic equation Zero-Flux Boundary Condition Structure Condition Entropy Formulation Multi-Step Approximation Nonlinear Semigroup Theories Integral and Mild Solution
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A Class of the Singularly Perturbed Boundary Value Problems for Elliptic Equation with a Super Surface of Turning Point in n-dimensional Space 被引量:6
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作者 王庚 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第1期41-46,共6页
In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theore... In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed. 展开更多
关键词 singular perturbation turning point elliptic equation
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The Singularly Perturbed Boundary Value Problems for Elliptic Equation with Turning Point 被引量:1
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作者 陈松林 莫嘉琪 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第3期12-16,共5页
The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary ... The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied. 展开更多
关键词 singular perturbation boundary value problem elliptic equation
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GLOBAL BOUND ON THE GRADIENT OF SOLUTIONS TO p-LAPLACE TYPE EQUATIONS WITH MIXED DATA
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作者 Minh-Phuong TRAN The-Quang TRAN Thanh-Nhan NGUYEN 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1394-1414,共21页
In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogene... In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest. 展开更多
关键词 gradient estimates p-Laplace quasilinear elliptic equation fractional maximal operators Lorentz-Morrey spaces
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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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Positive Solutions of a Semilinear Elliptic Equation with Coefficient That Changes Sign
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作者 马如云 姚庆六 李宝麟 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第4期10-14,共5页
We prove the existence of a positive solution to the problem-Δu=a(x)f(u), x∈Ω, u(x)=0,x∈Ω,where Ω is a bounded domain in R n with smooth boundary, a(x) is allowed to change sign.
关键词 elliptic equation positive solution Leray-Schauder fixed point theorem
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A CLASS OF SINGULARLY PERTURBED GENERALIZED BOUNDARY VALUE PROBLEMS FOR QUASI-LINEAR ELLIPTIC EQUATION OF HIGHER ORDER 被引量:19
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作者 MO Jia-qi(莫嘉琪) +1 位作者 OUYANG Cheng(欧阳成) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第3期372-378,共7页
The singularly perturbed generalized boundary value problems far the quasi- linear elliptic equation of higher order are considered. Under suitable conditions, the existence, uniqueness and asymptotic behavior of the ... The singularly perturbed generalized boundary value problems far the quasi- linear elliptic equation of higher order are considered. Under suitable conditions, the existence, uniqueness and asymptotic behavior of the generalized solution for the Dirichlet problems are studied. 展开更多
关键词 elliptic equation singular perturbation generalized solution
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Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation 被引量:9
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作者 张亮 张立凤 李崇银 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第2期403-410,共8页
By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic functio... By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions. 展开更多
关键词 generalized Boussinesq equation Boussinesq-Burgers equation Jacobian elliptic function modified mapping method
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The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term 被引量:10
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作者 套格图桑 斯仁到尔吉 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第12期2809-2818,共10页
By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of ... By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg de Vries (KdV) equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed. 展开更多
关键词 auxiliary equation KdV equation with variable coefficients KdV equation with a forcible term Jacobi elliptic function-like exact solutions
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INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS 被引量:14
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作者 刘岚喆 《Acta Mathematica Scientia》 SCIE CSCD 2005年第1期89-94,共6页
It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to ... It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w). 展开更多
关键词 Nondivergence elliptic equation generalized Morrey space commutator of singular integral operator Ap weight
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Efficient Numerical Solution of the Modified Mild-Slope Equation 被引量:12
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作者 潘军宁 左其华 王红川 《China Ocean Engineering》 SCIE EI 2000年第2期161-174,共14页
An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an im... An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an improved ADI method involving a relaxation factor is adopted to solve it. The method has the advantage of improving the numerical stability and convergence rate by properly determining the relaxation factor. The range of the relaxation factor making the differential scheme unconditionally stable is determined by stability analysis. Several verifications are performed to examine the accuracy of the present model. The numerical results coincide with the analytic solutions or experimental data very well and the computer time is reduced. 展开更多
关键词 WAVE mild-slope equation numerical solution stability REFRACTION DIFFRACTION REFLECTION
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Solving Nonlinear Wave Equations by Elliptic Equation 被引量:12
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作者 FUZun-Tao LIUShi-Da LIUShi-Kuo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2003年第5期531-536,共6页
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wav... The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method. 展开更多
关键词 elliptic equation Jacobi elliptic function nonlinear equation periodic wave solution
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Construction of doubly-periodic solutions to nonlinear partial differential equations using improved Jacobi elliptic function expansion method and symbolic computation 被引量:7
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作者 赵雪芹 智红燕 张鸿庆 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第10期2202-2209,共8页
Some doubly-periodic solutions of the Zakharov-Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function solutions to construct dou... Some doubly-periodic solutions of the Zakharov-Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function solutions to construct doubly-periodic solutions of the Zakharov-Kuznetsov equation, which has been derived by Gottwald as a two-dimensional model for nonlinear Rossby waves. When the modulus k →1, these solutions reduce to the solitary wave solutions of the equation. 展开更多
关键词 Jacobi elliptic function method doubly-periodic solutions Zakharov-Kuznetsov equation
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New Jacobian Elliptic Function Solutions to Modified KdV Equation: Ⅰ 被引量:9
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作者 YAN Zhen-Ya 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第8期143-146,共4页
An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu&#... An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations. 展开更多
关键词 MODIFIED KDV equation JACOBIAN elliptic function SOLITARY wave solution trigonometric functionsolution
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AN EXISTENCE THEOREM OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS ON R^N 被引量:3
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作者 唐春雷 《Acta Mathematica Scientia》 SCIE CSCD 1999年第3期289-292,共4页
An existent theorem is obtained for nonzero W-1,W-2(R-N) solutions of the following equations on R-N -Delta u + b(x)u = f(x,u), x is an element of R-N, where b is periodic for some variables and coercive for the other... An existent theorem is obtained for nonzero W-1,W-2(R-N) solutions of the following equations on R-N -Delta u + b(x)u = f(x,u), x is an element of R-N, where b is periodic for some variables and coercive for the others, f is superlinear. 展开更多
关键词 semilinear elliptic equation PERIODICITY COERCIVITY superlinearity critical point
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