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Weighted variation inequalities for differential operators and singular integrals in higher dimensions

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Science China Mathematics 2017年第8期60卷 1419-1442页

作者： MA Tao TORREA Jose L. XU QuanHua School of Mathematics and Statistics Wuhan University Departamento de Matemticas Universidad Autónoma de Madrid Institute for Advanced Study in Mathematics Harbin Institute of Technology Laboratoire de mathematiques Universite de Franche-Comte Institut Universitaire de France

We prove weighted q-variation inequalities with 2 详细信息

We prove weighted q-variation inequalities with 2

关键词： variation inequalities A_(p) weights differential operators singular integrals vector-valued variationin equalities

HILBERTIAN INVARIANCE PRINCIPLE FOR EMPIRICAL PROCESS ASSOCIATED WITH A MARKOV PROCESS

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Chinese Annals of Mathematics,Series B 2003年第1期24卷 1-16页

作者： JIANG YIWEN WU LIMING Department of Mathematics Wuhan University Wuhan 430072 China. Department of Mathematics Military Economic Academy 430035 Wuhan China.Laboratoire de Mathematiques Appliquees. CNRS-UMR 6620 Universite Blaise Pascal 63177 Aubiere

The authors establish the Hilbertian invariance principle for the empirical process of astationary Markov process, by extending the forward-backward martingale decomposition ofLyons-Meyer-Zheng to the Hilbert space va... 详细信息

关键词： Forward-backward martingale decomposition Functional central limit theorem or Donsker's invariance principle Empirical process

TIME-DELAY AND SPECTRAL DENSITY FOR STARK HAMILTONIANS(Ⅱ)——ASYMPTOTICS OF TRACE FORMULAE

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Chinese Annals of Mathematics,Series B 1991年第3期12卷 358-383页

作者： D.ROBERT 王雪平 Departement de mathematiques Universite de Nantes 44072 Nantes Cedex 03 France. Department of Mathematics Beijing University Beijing China.

This paper studies the Schrodinger operator with a homogeneous electric field of the form -△+x1+V（x）, where x= （x1,…, xn）∈Rn. It is proved that in the specctral representation of the free Stark Hamiltonian, the time-delay operator in scattering theory can be expressed in trems of scattering matrix and under reasonable assumptions on the decay of the potential V, the on-shell time-delay operator is of trace class and its trace is related to the local spectral density via an explicit integral formula. Some asymptotics for the trace are estabhshed when the energy tends to infinity.

关键词： infinity explicit Hamiltonian assumptions Stark decay 刁刀 derive kernel 二尹

Development of Residual Distribution Schemes for the Discontinuous Galerkin Method:The Scalar Case with Linear Elements

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Communications in Computational Physics 2009年第2期5卷 376-390页

作者： Remi Abgrall Chi-Wang Shu Institut de mathematiques and INRIA Universite Bordeaux I341 cours de la Liberation33405 Talence cedexFrance Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

In this paper,we reformulate the piecewise linear discontinuous Galerkin(DG)method for solving two dimensional steady state scalar conservation laws in the framework of residual distribution(RD)*** allows us to propose a new class of nonlinear stabilization that does not destroy the formal accuracy of the *** results are shown to demonstrate the behavior of this approach.

关键词： Discontinuous Galerkin schemes residual distribution schemes high order unstructured meshes

Numerical Blow-up for a Nonlinear Heat Equation

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Acta Mathematica Sinica,English Series 2011年第5期27卷 845-862页

作者： Firmin K. N'GOHISSE Theodore K. BONI Universite d'Abobo-Adjame UFR-SFA Departement de Mathematiques et Informatique 01 BP 1003 Abidjan 01 Cdte d'Ivoire Institut National Polytechnique Houphouet-Boigny de Yamoussoukro BP 1093 Yamoussoukro Cote d'Ivoire

This paper concerns the study of the numerical approximation for the following initialboundary value problem{ut-uzx=f（u）,t∈（0,1）,t∈（0,T） u（0,t）=0,t∈（0,1）,t∈（0,T） u（x,0）=u0（x）,x∈（0,1）where f（s） is a positive, increasing, C1 convex function for the nonnegative values of s, f（0）〉0, f∞ds/f（s）〈∞, u0∈C1（[0, 1]）, u0（0） = 0, u＇0（1）=0. We find some conditions under which the solution of a semidiscrete form of the above problem blows up in a finite time and estimate its semidiserete blow-up time. We also prove the convergence of the semidiscrete blow-up time to the theoretical one. A similar study has been also undertaken for a discrete form of the above problem. Finally, we give some numerical results to illustrate our analysis.

关键词： Semidiscretization blow-up numerical blow-up time nonlinear heat equations

Global hydrostatic approximation of the hyperbolic Navier-Stokes system with small Gevrey class 2 data In memory of Professor Geneviève Raugel

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Science China Mathematics 2022年第6期65卷 1109-1146页

作者： Marius Paicu Ping Zhang Institut de mathematiques de Bordeaux Universite BordeauxTalence 33405France Academy of Mathematics and Systems Science and Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

We investigate the hydrostatic approximation of a hyperbolic version of Navier-Stokes equations,which is obtained by using the Cattaneo type law instead of the Fourier law,evolving in a thin strip R×(0,ε).The formal limit of these equations is a hyperbolic Prandtl type *** first prove the global existence of solutions to these equations under a uniform smallness assumption on the data in the Gevrey class *** we justify the limit globally-in-time from the anisotropic hyperbolic Navier-Stokes system to the hyperbolic Prandtl system with such Gevrey class 2 *** with Paicu et al.(2020)for the hydrostatic approximation of the 2-D classical Navier-Stokes system with analytic data,here the initial data belongs to the Gevrey class 2,which is very sophisticated even for the well-posedness of the classical Prandtl system(see Dietert and GerardVaret(2019)and Wang et al.(2021));furthermore,the estimate of the pressure term in the hyperbolic Prandtl system gives rise to additional difficulties.

关键词： incompressible hyperbolic Navier-Stokes equations hydrostatic approximation hyperbolic Prandtl system

Neutral stochastic delay partial functional integro-differential equations driven by a fractional Brownian motion

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Frontiers of Mathematics in China 2013年第4期8卷 745-760页

作者： Tomas CARABALLO Mamadou Abdoul DIOP Dpto. Ecuaciones Diferenciales y Analisis Numerico Universidad de Sevilla Apdo. de Correos 1160 41080-Sevilla Spain Universite Gaston Berger de Saint-Louis UFR SAT Departement de Mathematiques 234 Saint-Louis Senegal

This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion BH, with Hurst parameter H E （1/2, 1）. We use the theory of resolvent operators developed by R. Grimmer to show the existence of mild solutions. An example is provided to illustrate the results of this work.

关键词： Resolvent operator C0-semigroup Wiener process mild solution fractional Brownian motion

Fixed points of n-valued maps on surfaces and the Wecken property a configuration space approach

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Science China Mathematics 2017年第9期60卷 1561-1574页

作者： GONCALVES Daciberg Lima GUASCHI John Departamento de Matemdtica&IME Universidade de Sao PauloSdo Paulo 05508-090Brazil Laboratoire de mathematiques Nicolas Oresme UMR CNRS 6139 UNICAENNormandie UniversiteCS 1403214032 Caen Cedex 5France

Abstract In this paper, we explore the fixed point theory of n-vaiued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane （resp. the 2-sphere S2） has the Wecken property for n-valued maps for all n ∈N （resp. all n ≥ 3）. In the case n = 2 and S2, we prove a partial result about the Wecken property. We then describe the Nielsen number of a non-split n-valued map φ ： X → X of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q：）→ X with a subset of the coordinate maps of a lift of the n-valued split map → q ： →X.

关键词： multivalued maps fixed points Wecken property Nielsen numbers braids configuration space

Maximum Principle for Nonlinear Cooperative Elliptic Systems on R^N

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Journal of Partial Differential Equations 2011年第3期24卷 264-280页

作者： LEADI Liamidi MARCOS Aboubacar Institut de mathematiques et de Sciences Physiques Universite d'Abomey Calavi

We investigate in this work necessary and sufficient conditions for having a Maximum Principle for a cooperative elliptic system on the whole R^N. Moreover, we prove the existence of solutions by an approximation meth... 详细信息

关键词： Elliptic systems p-Laplacian operator principal eigenvalues Leray-Schauder fixedpoint approximation method.