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941.
M. M. Cavalcanti V. N. Domingos Cavalcanti J. A. Soriano L. A. Medeiros 《Southeast Asian Bulletin of Mathematics》2000,24(2):183-199
In this paper, we study a hyperbolic model based on the equation
with nonlinear boundary conditions given by
.We prove the existence and the uniqueness of global solutions. Also, we obtain the uniform decay of the energy without control of its derivative sign.AMS Subject Classification (2000), 35L05, 35L70, 35B40 相似文献
942.
袁锦昀 《应用数学学报(英文版)》2000,16(2):130-139
1.IntroductionThegeneralizedleastsquaresproblem,definedasmin(Ax--b)"W--'(Ax--b),(1.1)xacwhereAERm",m>n,bERm,andWERm'misasymmetricandpositivedefinitematrix,isfrequentlyfoundwhensolvingproblemsinstatistics,engineeringandeconomics.Forexample,wegetgeneralizedleastsquaresproblemswhensolvingnonlinearregressionanalysisbyquasi-likelihoodestimation,imagereconstructionproblemsandeconomicmodelsobtainedbythemaximumlikelihoodmethod(of.[1,21).Paige[3,4]investigatestheproblemexplicitly.Hechangestheorig… 相似文献
943.
We consider a one-dimensional incompressible flow through a porous medium undergoing deformations such that the porosity and the hydraulic conductivity can be considered to be functions of the flux intensity. The medium is initially dry and we neglect capillarity, so that a sharp wetting front proceeds into the medium. We consider the open problem of the continuation of the solution possibly in the case of onset of singularities, which can be interpreted as a local collapse of the medium. In particular we analyze the case in which the boundary pressure has a piecewise constant derivative. 相似文献
944.
51. IntroductionLet fi C Re (n = 1,2) be a bounded smooth domain. Consider the following nonhomogeneous initial-boundary value problem for the unsaturated Landau-Lifshitz systems offerromagnetic spin chain with Gilbert damping constant afl > 0,where adZ is the exchange constallt, u = (u', u', u'), "o(x) is smooth and satisfies the unsaturated condition, i.e., Ilo(~)I gi constant, and in IVuol' < co, "o(x)IOn = op(x). DenoteW(x) = luo(x)I. We assume 0 < m = mane < M ~ mpxW. Throughout t… 相似文献
945.
The evolution Boussinesq equations describe the evolution of the temperature and velocity fields of viscous incompressible Newtonian fluids. Very often, they are a reasonable model to render relevant phenomena of flows in which the thermal effects play an essential role. In the paper we prescribe non-Dirichlet boundary conditions on a part of the boundary and prove the existence and uniqueness of solutions to the Boussinesq equations on a (short) time interval. The length of the time interval depends only on certain norms of the given data. In the proof we use a fixed point theorem method in Sobolev spaces with non-integer order derivatives. The proof is performed for Lipschitz domains and a wide class of data. 相似文献
946.
Petr Knobloch 《Applications of Mathematics》2000,45(2):99-129
We investigate a finite element discretization of the Stokes equations with nonstandard boundary conditions, defined in a bounded three-dimensional domain with a curved, piecewise smooth boundary. For tetrahedral triangulations of this domain we prove, under general assumptions on the discrete problem and without any additional regularity assumptions on the weak solution, that the discrete solutions converge to the weak solution. Examples of appropriate finite element spaces are given. 相似文献
947.
We introduce a new family of semiiterative schemes for the solution of ill-posed linear equations with selfadjoint and indefinite operators. These schemes avoid the normal equation system and thus benefit directly from the structure of the problem. As input our method requires an enclosing interval of the spectrum of the indefinite operator, based on some a priori knowledge. In particular, for positive operators the schemes are mathematically equivalent to the so-called -methods of Brakhage. In a way, they can therefore be seen as appropriate extensions of the -methods to the indefinite case. This extension is achieved by substituting the orthogonal polynomials employed by Brakhage in the definition of the -methods by appropriate kernel polynomials. We determine the rate of convergence of the new methods and establish their regularizing properties. 相似文献
948.
This paper deals with the iterative solution of stage equations which arise when some fully implicit Runge-Kutta methods,
in particular those based on Gauss, Radau and Lobatto points, are applied to stiff ordinary differential equations. The error
behaviour in the iterates generated by Newton-type and, particularly, by single-Newton schemes which are proposed for the
solution of stage equations is studied. We consider stiff systems y'(t) = f(t,y(t)) which are dissipative with respect to
a scalar product and satisfy a condition on the relative variation of the Jacobian of f(t,y) with respect to y, similar to
the condition considered by van Dorsselaer and Spijker in [7] and [17]. We prove new convergence results for the single-Newton
iteration and derive estimates of the iteration error that are independent of the stiffness. Finally, some numerical experiments
which confirm the theoretical results are presented.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
949.
Robert Deville Julian P. Revalski 《Proceedings of the American Mathematical Society》2000,128(4):1117-1124
We prove that in several classes of optimization problems, including the setting of smooth variational principles, the complement of the set of well-posed problems is -porous.
950.
Twin solutions to singular boundary value problems 总被引:5,自引:0,他引:5
Ravi P. Agarwal Donal O'Regan 《Proceedings of the American Mathematical Society》2000,128(7):2085-2094
In this paper we establish the existence of two nonnegative solutions to singular and singular focal boundary value problems. Our nonlinearity may be singular at , and/or .