共查询到20条相似文献,搜索用时 0 毫秒
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Tie Zhang Datao Shi Zhen Li 《计算数学(英文版)》2008,26(5):689-701
In this paper, a discontinuous finite element method for the positive and symmetric, first-order hyperbolic systems (steady and nonsteady state) is constructed and analyzed by using linear triangle elements, and the O(h^2)-order optimal error estimates are derived under the assumption of strongly regular triangulation and the Ha-regularity for the exact solutions. The convergence analysis is based on some superclose estimates of the interpolation approximation. Finally, we discuss the Maxwell equations in a two-dimensional domain, and numerical experiments are given to validate the theoretical results. 相似文献
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一阶双曲问题的有限元后验误差估计至今没有得到很好的解决.本文对d维区域上一阶双曲问题的k次间断有限元逼近提出了一种新的后验误差分析方法, 进而建立了间断有限元解在DG范数下(强于L2范数)基于误差余量型的后验误差估计. 数值计算验证了本文理论分析的有效性. 本文方法也适用于其他变分问题有限元逼近的后验误差分析. 相似文献
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EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH ZERO EIGENVALUES*** 总被引:4,自引:0,他引:4
For a class of mixed initial-boundary value problem for general quasilinear hyperbolic sys-tems with zero eigenvalues, the authors establish the local exact controllability with boundary controls acting on one end or on two ends and internai controls acting on a part of equations in the system. 相似文献
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ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM 下载免费PDF全文
This paper is a continuation of the authors'previous paper[1].In this paper the authorsprove,assuming additional conditions on the initial data,some results about the existence anduniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolicsystem a_t+(au)_x_2au/x=0,u_t+1/2(a~2+u~2)_x=0,x>0,t≥0. 相似文献
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Zhou Yi 《数学年刊B辑(英文版)》1997,18(2):223-232
LOCALEXISTENCETHEOREMFORFIRSTORDERSEMILINEARHYPERBOLICSYSTEMSINSEVERALSPACEDIMENSIONSZHOUYIAbstractThispaperstudiesfirstorde... 相似文献
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REGULARIZATION OF AN ILL-POSED HYPERBOLIC PROBLEM AND THE UNIQUENESS OF THE SOLUTION BY A WAVELET GALERKIN METHOD 下载免费PDF全文
We consider the problem K(x)u xx = u tt , 0 < x < 1, t ≥ 0, with the boundary condition u(0,t) = g(t) ∈ L 2 (R) and u x (0, t ) = 0, where K(x) is continuous and 0 < α≤ K (x) < +∞. This is an ill-posed problem in the sense that, if the solution exists, it does not depend continuously on g. Considering the existence of a solution u(x, ) ∈ H 2 (R) and using a wavelet Galerkin method with Meyer multiresolution analysis, we regularize the ill-posedness of the problem. Furthermore we prove the uniqueness of the solution for this problem. 相似文献
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1IntroductionAs we well know,the study of the local existence of discontinuous solutions to semilinearor quasi-linear hyperbolic systems in higher dimension spaces has attracted considerable at-tention of many well-known mathematicians,thanks to A.Majda’… 相似文献
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ON THE CAUCHY PROBLEM OF TRANSPORTATION EQUATIONS 总被引:1,自引:0,他引:1
1.IntroductionInthepreselltpaper,weconsiderthetransportationsystemwithinitialdatawherepanduaredensityandvelocityrespectively.Thesystemofconservationlaws(1.1)describesthefluidmechanicswithconstalltpressuxe,whichisusedinplasmaphysicswherepressureisassumedtobeaconstant.Thissystemisnon--strictlyhyperbolicwithadoubleeigenvalueAl~AZ=albothAl,AZbeinglinearlydegenerate.AndtheCauchyproblemforthissystemisnotwell-posedintheclassofmeasurableandboundedfunctions(see[3]).Inthepresentpaper,weintroduceanew… 相似文献
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SEMI-GLOBAL $C^1$ SOLUTION TO THE MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS 总被引:6,自引:2,他引:6
By means of an equivalent invariant form of boundary conditions, the authors get the existence and uniqueness of semi-global C^1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with general nonlinear boundary conditions. 相似文献
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GLOBAL EXISTENCE OF WEAKLY DISCONTIN UOUS SOLUTIONS TO THE CAUCHY PROBLEM WITH A KIND OF NON-SMOOTH INITIAL DATA FOR QUASILINEAR HYPERBOLIC SYSTEMS 总被引:4,自引:0,他引:4 下载免费PDF全文
The authors consider the Cauchy problem with a kind of non-smooth initial datafor quasilinear hyperbolic systems and obtain a necessary and sufficient condition toguarantee the existence and uniqueness of global weakly discontinuous solution. 相似文献
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ON THE ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT APPROXIMATION TO THE OBSTACLE PROBLEM 总被引:2,自引:0,他引:2
Lie-hengWang 《计算数学(英文版)》2003,21(4):481-490
This paper is devoted to analysis of the nonconforming element approximation to the obstacle problem, and improvement and correction of the results in [11], [12]. 相似文献
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By cone theory and the fixed point index,we study the existence of positive solutions to a three-order boundary value problem with dependence on the first order derivative. 相似文献
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In this paper, we give some results on the blow-up behaviors of the solution to the mixed problem for some higher nonlinear hyperbolic evolution equation in finite time. By introducing the "blow-up factor K(u,ut)" we get some new results, which generalize the conclusions of [3] and [4]. 相似文献
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叶耀军 《数学物理学报(B辑英文版)》2005,25(4):703-709
The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div(|▽u|p-2▽u)= |u|mu, (x,t) ∈ [0, ∞) ×Ωwith p > 2 and m > 0. He deals with the global solutions by D.H.Sattinger's potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded,the global nonexistence of solutions is verified by using the analysis method. 相似文献