检索结果-南通市图书馆

Global regularity for 3D magneto-hydrodynamics equations with only horizontal dissipation

在线全文

学校读者我要写书评

暂无评论

Frontiers of Mathematics in China 2019年第1期14卷 149-175页

作者： Yutong WANG Weike WANG School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 220104 China Institute of Natural Sciences Shanghai Jiao Tong University Shanghai 220104 China

We investigate the Cauchy problem for the 3D magneto-hydrodynamics equations with only horizontal dissipation for the small initial data. With the help of the dissipation in the horizontal direction and the structure of the system, we analyze the properties of the decay of the solution and apply these decay properties to get the global regularity of the solution. In the process, we mainly use the frequency decomposition in Green's function method and energy method.

关键词： Magneto-hydrodynamics (MHD) equations degenerate dissipation global solution Green's function method frequency decomposition method

SUPERCONVERGENCE ANALYSIS FOR TIME-FRACTIONAL DIFFUSION equations WITH NONCONFORMING MIXED FINITE ELEMENT METHOD

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2019年第4期37卷 488-505页

作者： Houchao Zhang Dongyang Shi School of Mathematics and Statistics Pingdingshan University Pingdingshan 467000 China School of Mathematics and Statistics Zhengzhou University Zhengzhou 450001 China

In this paper, a fully discrete scheme based on the LI approximation in temporal direction for the fractional derivative of order in (0,1) and nonconforming mixed finite element method (MFEM) in spatial direction is established. First, we prove a novel result of the consistency error estimate with order O(h^2)of EQ1^rot element (see Lemma 2.3). Then, by using the proved character of EQ1^rot element, we present the superconvergent estimates for the original variable u in the broken H^1-norm and the flux →p =△u in the (L^2)^2-norm under a weaker regularity of the exact solution. Finally, numerical results are provided to confirm the theoretical analysis.

关键词： Nonconforming MFEM LI method Time-fractional diffusion equations Superconvergence

Mass conservational equations at the solid-liquid interface and self-organization model of some growth layers

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China(Technological Sciences) 1997年第4期40卷 350-360页

作者：吴金平李才伟肖文丁杨问华 Department of Applied Chemistry China University of Geosciences Wuhan 430074 China Institute of Geochemistry China University of GeosciencesWuhan 430074China

equations of interface mass conservation of nonsteady-state crystalline growth process are established. These equations provide a basic mathematical model for the strict treatment of the non-equilibrium and nonlinear problems in the formation of crystalline growth layers. A kinetic model is built of nonlinear self-catalytic crystalline reaction for the formation of impurity growth layer in flux single crystalline growth. Discussion is made, from the formation of self-organization pattern, on some origins of growth layers that are difficult to explain by existing

关键词： crystal growth mass conservational equations growth layer self-organization.

Convergence to diffusion waves for solutions of Euler equations with time-depending damping on quadrant

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2019年第1期62卷 33-62页

作者： Haibo Cui Haiyan Yin Changjiang Zhu Limei Zhu School of Mathematical Sciences Huaqiao University School of Mathematics South China University of Technology

This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant(x,t)∈R^+×R^+,with the null-Dirichlet boundary condition or the null-Neumann boundary condition on u. We show that the corresponding initial-boundary value problem admits a unique global smooth solution which tends timeasymptotically to the nonlinear diffusion wave. Compared with the previous work about Euler equations with constant coefficient damping, studied by Nishihara and Yang(1999), and Jiang and Zhu(2009, Discrete Contin Dyn Syst), we obtain a general result when the initial perturbation belongs to the same space. In addition,our main novelty lies in the fact that the cut-off points of the convergence rates are different from our previous result about the Cauchy problem. Our proof is based on the classical energy method and the analyses of the nonlinear diffusion wave.

关键词： Euler equations with time-depending damping nonlinear diffusion waves initial-boundary value problem decay estimates

LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR equations WITH WEIGHTS

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2019年第2期39卷 357-368页

作者： Phuong LE Vu HO Department of Mathematical Economics Banking University of Ho Chi Minh City Division of Computational Mathematics and Engineering Institute for Computational ScienceTon Duc Thang University Faculty of Mathematics and Statistics Ton Duc Thang University

This paper is devoted to the quasilinear equation ■where p > 2,Ω is a(bounded or unbounded) domain of R^N,w_1,w_2 are nonnegative continuous functions and f is an increasing function. We establish a Liouville type theorem for nontrivial stable solutions of the equation under some mild assumptions on Ω,w_1, w_2 and f, which extends and unifies several results on this topic.

关键词： quasilinear equations stable solutions nonexistence Liouville theorems

EXISTENCE AND STABILITY RESULTS FOR GENERALIZED FRACTIONAL DIFFERENTIAL equations

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2020年第1期40卷 141-154页

作者： A.BEN MAKHLOUF D.BOUCENNA M.A.HAMMAMI Department of Mathematics College of SciencesJouf UniversityAljoufSaudi Arabia Department of Mathematics Faculty of Sciences of SfaxBP 11713000 SfaxTunisia Higher School for Professors of Technological Education SkikdaAlgeria

In this paper,a sufficient conditions to guarantee the existence and stability of solutions for generalized nonlinear fractional differential equations of orderα(1<α<2)are given.The main results are obtained by using Krasnoselskii's fixed point theorem in a weighted Banach space.Two examples are given to demonstrate the validity of the proposed results.

关键词： nonlinear fractional differential equations stability analysis generalized fractional derivative Krasnoselskii's fixed point theorem

LIOUVILLE TYPE THEOREM FOR THE STATIONARY equations OF MAGNETO-HYDRODYNAMICS

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2019年第2期39卷 491-497页

作者： Simon SCHULZ Mathematical Institute University of Oxford

We show that any smooth solution(u, H) to the stationary equations of magnetohydrodynamics belonging to both spaces L^6(R^3) and BMO^(-1)(R^3) must be identically zero.This is an extension of previous results, all of which systematically required stronger integrability and the additional assumption ▽u, ▽H∈L^2(R^3), i.e., finite Dirichlet integral.

关键词： Liouville theorem Caccioppoli inequality Navier-Stokes equations MHD

EULER SCHEME FOR FRACTIONAL DELAY STOCHASTIC DIFFERENTIAL equations BY ROUGH PATHS TECHNIQUES

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2019年第3期39卷 747-763页

作者： Johanna GARZON Samy TINDEL Soledad TORRES Departamento de Matematicas Universidad Nacional de ColombiaBogota D.C.Colombia Department of Mathematics Purdue University150 N.University StreetW.LafayetteIN 47907USA Facultad de Ingenierza CIMF AV Universidad de ValparaisoCasilla 123-V4059 ValparaisoChile

In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(1/2,1). In order to prove convergence, we use rough paths techniques. Theoretical bounds are established and numerical simulations are displayed.

关键词： Fractional Brownian motion stochastic differential equations rough paths,discrete time approximation

The Cauchy problem for a class of nonlinear degenerate parabolic-hyperbolic equations

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2019年第5期62卷 839-852页

作者： Hua Chen Jinpeng Zhan Xin Hu School of Mathematics and Statistics and Computational Science Hubei Key Laboratory Wuhan University

In this article, we prove a general existence theorem for a class of nonlinear degenerate parabolichyperbolic equations. Since the regions of parabolicity and hyperbolicity are coupled in a way that depends on the solution itself, there is almost no hope of decoupling the regions and then taking into account the parabolic and the hyperbolic features separately. The existence of solutions can be obtained by ?nding the limit of solutions for the regularized equation of strictly parabolic type. We use the energy methods and vanishing viscosity methods to prove the local existence and uniqueness of solution.

关键词： parabolic-hyperbolic equations energy methods vanishing viscosity methods