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Analysis in Theory and Applications 2013年第3期29卷 234-254页

作者： Y. Akdim J. Bennouna A. Bouajaja M.Mekkour UniversitSidi Mohamed Ben Abdellah Laboratoire LAMAFacultdes Sciences Dhar-MahrazFèsMorocco FacultPoly-disciplinaire de TazaB.P 1223 Taza GareMaroc

We prove an existence result without assumptions on the growth of some nonlinear terms, and the existence of a renormalized solution. In this work, we study the existence of renormalized solutions for a class of nonlinear parabolic systems with three unbounded nonlinearities, in the form { b1（x,u1）/ t-div（a（x,t,u1,Du1））＋div（Ф1（u1））＋f1（x,u1,u2）=O in Q, b2（x,u2）/ t-div（a（x,t,u2,Du2））＋div（Ф2（u2））＋f2（x,u1,u2）=O in Q in the framework of weighted sobolev spaces, where b（x,u） is unbounded function on u, the Carath6odory function ai satisfying the coercivity condition, the general growth condition and only the large monotonicity, the function Фi is assumed to be continuous on ]R and not belong to （Lloc1（Q））N.

关键词： Nonlinear parabolic system existence truncation weighted sobolev space renor-malized solution.

weighted and Resonance Quasilinear Elliptic Problems with Jumping Nonlinearities

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Acta Mathematicae Applicatae Sinica 2018年第2期34卷 438-450页

作者： Gao JIA Chun-yan DAI Jie CHEN College of Science University of Shanghai for Science and Technology Shanghai 200093 China Shanghai Tianshan Second Middle School Shanghai 200336 China Xiang Yifu Rong Second Middle School Changsha 410000 China

In this paper, the existence of a nontrivial solution for a class of quasilinear elliptic equations with a disturbance term in a weighted sobolev space is proved. The proofs rely on Galerkin method, Brouwer＇s theorem... 详细信息

关键词： weighted sobolev space quasilinear elliptic equation Oalerkin method

GEVREY REGULARITY WITH WEIGHT FOR INCOMPRESSIBLE EULER EQUATION IN THE HALF PLANE

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Acta Mathematica Scientia 2017年第4期37卷 1115-1132页

作者：程峰李维喜徐超江 School of Mathematics and Statistics Wuhan UniversityWuhan 430072China School of Mathematics and Statistics and Computational Science Hubei Key LaboratoryWuhan UniversityWuhan 430072China

In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L;-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.

关键词： Gevrey class regularity incompressible Euler equation weighted sobolev space

The Existence and Uniqueness of a New Boundary Value Problem(Type of Problem“E”)for a Class of Semi Linear(Power Type Nonlinearities)Mixed Hyperbolic-Elliptic System Equations of Keldysh Type with Changing Time Direction

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 763-777页

作者： Mahammad A.NURMAMMADOV Shemakhi Astrophysical Observatory named after Nasreddin Tusi of the Azerbaijan's Ministry of Science and EducationAZ-5626ShemakhadistrictPirkuliAzerbaijan

In present work studied the new boundary value problem for semi linear(Power-type nonlinearities)system equations of mixed hyperbolic-elliptic Keldysh type in the multivariate dimension with the changing time *** problem and equation belongs to the modern level partial differential *** methods of functional analysis,topological methods,“ε”-*** continuation by the parameter at the same time with aid of a prior estimates,under assumptions conditions on coefficients of equations of system,the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted sobolev's *** this work one of main idea consists of show that the new boundary value problem which investigated in case of linear system equations can be well-posed when added nonlinear terms to this linear system equations,moreover in this case constructed new weithged spaces,the identity between of strong and weak solutions is established.

关键词： changing time direction weighted sobolev space equation of mixed type strong weak and regular solution eqution of Keldysh type

A CRITERION FOR DISCRETE SPECTRUM OF A CLASS OF DIFFERENTIAL OPERATORS

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Journal of Systems Science & Complexity 2003年第1期16卷 95-100页

作者： WEI Guangsheng(Research Center for Applied Mathematics and Institute for Information and Systems Science, Xi’anJiaotong University, Xi’an 710049, China) Research Center for Applied Mathematics and Institute for Information and Systems Science Xi'an Jiaotong University Xi'an 710049

In this paper,a sufficient and necessary condition is obtained to ensure that the spectrum of a class of 2n-order weighted differential operators is *** proof is based on the method of certain weighted sobolev spaces ... 详细信息

关键词： Spectrum weighted sobolev space compactly embedding.

INTERPOLATION INEQUALITIES AND DECAY ESTIMATES FOR DERIVATIVES

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Analysis in Theory and Applications 2000年第3期16卷 10-31页

作者： Lu Xuguang (Tsinghua University , China) Department of Mathematics and Science Tsinghua University Beijing China

Under the only assumption of the cone property for a given domain Ω?R n, it is proved that interpolation inequalities for intermediate derivatives of functions in the sobolev spaces Wm,p (Ω) or even in some weighted Sobolve spaces W w m,p (Ω) still hold. That is, the usual additional restrictions that Ω is bounded or has the uniform cone property are both removed. The main tools used are polynomial inequalities, by which it is also obtained pointwise version interpolation inequalities for smooth and analytic functions. Such pointwise version inequalities give explicit decay estimates for derivatives at infinity in unbounded domains which have the cone property. As an application of the decay estimates, a previous result on radial basis function approximation of smooth functions is extended to the derivative-simultaneous approximation.

关键词： Orthogonal Matrix Decay Estimate weighted sobolev space Interpolation Inequality Cone Versus

RATE OF CONVERGENCE FOR MEYER-KONIG AND ZELLER OPERATORS WITH JACOBI-WEIGHTS

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Approximation Theory and Its Applications 2002年第3期18卷 52-64页

作者： SongRuying XuangPeicai 等 TaiyuanTeachersCollege China ShaoxingCollegeofArtsandScience China

We point out that the Meyer-Konig and Zeller operator Mn (f;x) are unbounded in usual Jacobi weighted norm at first, and then we consider the weighted approximation by Mn(f;x) by a new norm and obtain the characteriza... 详细信息

关键词： Uniform Approximation weighted sobolev space Inverse Theorem Characterization Problem Youth Foundation

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一类非定常流的奇异有限元分析

高等学校计算数学学报 2000年第3期22卷 232-239页

作者：王光辉杨晓忠 100084 102206 华北电力大学（北京）基础科学系!北京清华大学计算机科学与技术系!北京

In this paper, we study a kind of axial symmetry nonsteady flowing in bi-ological fluid mechanics. lt is of the strange character of nonlinear PDE. An effcientFEM analyses is presented. FEM schemes are established. Mo... 详细信息

关键词： Finite elemental method with strange character weighted sobolev space L2 and H21 norm error estimations