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91.
IntroductionTheshallowwaterequationsareanimportantmathematicalmodelforavarietyofprobleminhydraulicengineering .Inrecentyears,therehasbeeninterestinthenumericalsolutionfortheshallowwaterequations.Thenumericalsimulationsfortheshallowwaterequationsystemcanbeappliedtomanypurposes .First,itcanserveasameansformodelingtidalfluctuationsforthosenterestedincapturingtidalenergyforcommercialpurposes.Secondly ,thesesimulationscanbeusedtocomputetidalrangesandsurgessuchashurricanesandtsunamiscausedbyextreme…  相似文献   
92.
In an essentially statistical approach to statistical mechanics, it is seen that the Gauss principle of the arithmetic mean may be taken as the starting point. The equations from which the subject can be built up are deduced from the Gauss principle of the arithmetic mean.  相似文献   
93.
The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.  相似文献   
94.
We obtain curvature estimates for certain stable minimalhypersurfaces in R 4 and R 5without using volume bounds. It follows that if M is acomplete stable minimal hypersurface in R 4 orR 5, then M is a hyperplane whenM intersects each extrinsic ball in, at most,N-components.  相似文献   
95.
1 IntroductionThe K-S equation represents a class of pattern formation equations.It has beenstudied extensively in recent years,both in the context of inertial manifolds and finite-di-mensional attractors as well as in numerical simulations of system dynamical behaviour( see[2 ,4 ,7-1 0 ] ) .Despite many studies of dynamical behaviour of the K_ Sequation,the steady-state analysis of the equation has not been thoroughly carried out,which ispractically important and theoretically interesting.…  相似文献   
96.
In this paper, the existence and uniqueness of the time-periodic solutions to the Ginzburg-Landau-BBM equations are proved by using a priori estimates and Leray-Schauder fixed point theorem.  相似文献   
97.
In this paper, we consider the pressure projection stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality problem of the second kind with the Stokes operator. The H1 and L2 error estimates for the velocity and the L2 error estimate for the pressure are obtained. Finally, the numerical results are displayed to verify the theoretical analysis.  相似文献   
98.
In this paper, we introduce two novel split least-squares mixed element procedures for pseudo-parabolic equations. By selecting the least-squares functional properly, each procedure can be split into two independent symmetric positive definite sub-procedures. One of sub-procedures is for the primitive unknown variable u, which is the same as the standard Galerkin finite element procedure and the other is for the introduced flux variable σ. Optimal order error estimates are developed. A numerical example is given to show the efficiency of the introduced schemes.  相似文献   
99.
We describe a technique for a posteriori error estimates suitable to the optimal control problem governed by the evolution equations solved by the method of lines. It is applied to the control problem governed by the parabolic equation, convection-diffusion equation and hyperbolic equation. The error is measured with the aid of the L2-norm in the space-time cylinder combined with a special time weighted energy norm.  相似文献   
100.
Shumin Li 《Applicable analysis》2013,92(11):2335-2356
In this article, we consider Maxwell's equations in an isotropic, inhomogeneous and non-stationary medium. We discuss an inverse problem of determining the t-independent components of the coefficients ?, μ in the constitutive relations from a finite number of interior measurements. We prove a Lipschitz stability estimate for the inverse problem by applying the argument on the basis of Carleman estimate.  相似文献   
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