共查询到17条相似文献,搜索用时 15 毫秒
1.
Mu Fa Chen 《数学学报(英文版)》2013,29(1):1-32
This paper studies the Hardy-type inequalities on the intervals (may be infinite) with two weights, either vanishing at two endpoints of the interval or having mean zero. For the first type of inequalities, in terms of new isoperimetric constants, the factor of upper and lower bounds becomes smaller than the known ones. The second type of the inequalities is motivated from probability theory and is new in the analytic context. The proofs are now rather elementary. Similar improvements are made for Nash inequality, Sobolev-type inequality, and the logarithmic Sobolev inequality on the intervals. 相似文献
2.
In this paper, we obtain some new Lyapunov-type inequalities for a class of higher-order linear differential equations with anti-periodic boundary value condition, the results of this paper are new and generalize and improve some early results in the literature. 相似文献
3.
Belen Lpez Juan Rocha Kishin Sadarangani 《Mathematical Methods in the Applied Sciences》2019,42(1):49-58
In this paper, Lyapunov‐type inequalities are derived for a class of fractional boundary value problems with integral boundary conditions. As an application, we obtain a lower bound for the eigenvalues of corresponding equations. 相似文献
4.
Oscillation of a quasilinear impulsive delay parabolic equation with two different boundary conditions 总被引:1,自引:0,他引:1
In this paper, we discuss the oscillation for a class of quasilinear impulsive delay parabolic equations with two different boundary conditions and obtain several oscillation criteria. 相似文献
5.
Kanittha Chompuvised Ampon Dhamacharoen 《Applied mathematics and computation》2011,217(24):10355-10360
This paper focuses on solving the two point boundary value problem, in which boundary conditions are systems of nonlinear equations. The shooting method was used together with a combination of Newton’s method and Broyden’s method, to update the initial values of the differential equations. The experiments showed that the proposed method performed well, in the sense that the overall amount of work was less than that of the Newton Shooting method. 相似文献
6.
This paper establishes a global Carleman inequality of parabolic equations with mixed boundary conditions and an estimate of the solution. Further, we prove exact controllability of the equation by controls acting on an arbitrarily given subdomain or subboundary. 相似文献
7.
Xuan-ru Lu Guang-Hua Gao Zhi-Zhong Sun 《Numerical Methods for Partial Differential Equations》2023,39(1):447-480
In this paper, the fourth-order parabolic equations with different boundary value conditions are studied. Six kinds of boundary value conditions are proposed. Several numerical differential formulae for the fourth-order derivative are established by the quartic interpolation polynomials and their truncation errors are given with the aid of the Taylor expansion with the integral remainders. Effective difference schemes are presented for the third Dirichlet boundary value problem, the first Neumann boundary value problem and the third Neumann boundary value problem, respectively. Some new embedding inequalities on the discrete function spaces are presented and proved. With the method of energy analysis, the unique solvability, unconditional stability and unconditional convergence of the difference schemes are proved. The convergence orders of derived difference schemes are all O(τ2 + h2) in appropriate norms. Finally, some numerical examples are provided to confirm the theoretical results. 相似文献
8.
We establish the wellposedness of the time‐independent Navier–Stokes equations with threshold slip boundary conditions in bounded domains. The boundary condition is a generalization of Navier's slip condition and a restricted Coulomb‐type friction condition: for wall slip to occur the magnitude of the tangential traction must exceed a prescribed threshold, independent of the normal stress, and where slip occurs the tangential traction is equal to a prescribed, possibly nonlinear, function of the slip velocity. In addition, a Dirichlet condition is imposed on a component of the boundary if the domain is rotationally symmetric. We formulate the boundary‐value problem as a variational inequality and then use the Galerkin method and fixed point arguments to prove the existence of a weak solution under suitable regularity assumptions and restrictions on the size of the data. We also prove the uniqueness of the solution and its continuous dependence on the data. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
9.
We propose and analyze a two‐level method of discretizing the nonlinear Navier‐Stokes equations with slip boundary condition. The slip boundary condition is appropriate for problems that involve free boundaries, flows past chemically reacting walls, and other examples where the usual no‐slip condition u = 0 is not valid. The two‐level algorithm consists of solving a small nonlinear system of equations on the coarse mesh and then using that solution to solve a larger linear system on the fine mesh. The two‐level method exploits the quadratic nonlinearity in the Navier‐Stokes equations. Our error estimates show that it has optimal order accuracy, provided that the best approximation to the true solution in the velocity and pressure spaces is bounded above by the data. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 26–42, 2001 相似文献
10.
通过引入伸展变量和非常规的渐近序列{∈}),运用合成展开法,对一类具非线性边界条件的非线性高阶微分方程的奇摄动问题构造了形式渐近解,再运用微分不等式理论证明了原问题解的存在性及所得渐近近似式的一致有效性. 相似文献
11.
M.R. Grossinho F.M. Minhós A.I. Santos 《Journal of Mathematical Analysis and Applications》2005,309(1):271-283
In this work we provide an existence and location result for the third-order nonlinear differential equation
u?(t)=f(t,u(t),u′(t),u″(t)), 相似文献
12.
Numerical study of mixed convection flow of a micropolar fluid towards permeable vertical plate with convective boundary condition 下载免费PDF全文
Ch. RamReddy T. Pradeep D. Srinivasacharya 《Journal of Applied Analysis & Computation》2016,6(2):254-270
In this article, the mixed convective flow of a micropolar fluid along a permeable vertical plate under the convective boundary condition is analyzed. The scaling group of transformations is applied to get the similarity representation of the system of partial differential equations of the problem and then the resulting equations are solved by using Spectral Quasi-Linearisation Method. This study reveals that the dual solutions exists for certain values of mixed convection parameter. The outcomes are analyzed with dual solutions in detail. Effects of micropolar parameter, Biot number and suction/injection parameters on different flow profiles are discussed and depicted graphically. 相似文献
13.
By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential
equations with linear functional boundary conditions. The nonlinear term f(t, u) is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0,1] positive solutions as well as the C
1[0, 1] positive solutions. 相似文献
14.
István Faragó Róbert Horváth Sergey Korotov 《Numerical Methods for Partial Differential Equations》2011,27(3):702-720
In this article, we derive and discuss sufficient conditions for providing validity of the discrete maximum principle for nonstationary diffusion‐reaction problems with mixed boundary conditions, solved by means of simplicial finite elements and the θ time discretization method. The theoretical analysis is supported by numerical experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
15.
E. E. Bukzhalev A. B. Vasil’eva 《Computational Mathematics and Mathematical Physics》2007,47(3):407-419
The solution to a singularly perturbed parabolic equation with internal and boundary layers whose stretched variables may depend on different powers of the perturbation parameter is considered. An asymptotic representation of the solution is constructed and substantiated, and its stability is proved. 相似文献
16.
Miloslav Foistauer Karel Najzar Vcronika Sobotíková 《Numerical Functional Analysis & Optimization》2013,34(9-10):835-851
The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition. The existence and uniqueness of the solution of the continuous pioblem is a consequence of the monotone operator theory. The main attention is paid to the investigation of the finite element approximation using numeriral integration for the evaluation of boundary integrals. The error estimates for the solution of the discrete finite element problem are derived 相似文献
17.
B. V. Pal’tsev I. I. Chechel’ 《Computational Mathematics and Mathematical Physics》2006,46(5):820-847
The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 103. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ~ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ~ 5 × 103. 相似文献