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281.
E.M.E.ZAYED 《数学学报(英文版)》2003,19(4):679-694
The asymptotic expansions of the trace of the heat kernel θ(t)=∑^∞v=1^exp(-tλv) for small positive t,where {λv} are the eigenvalues of the negative Laplacian -△n=-∑^ni=1(D/Dx^1)^2 in R^2(n=2 or 3),are studied for a general annular bounded domain Ω with a smooth inner boundary DΩ1 and a smooth outer boundary DΩ2,where a finite number of piecewise smooth Robin boundary conditions(D/Dnj γh)Ф=0 on the components Гj(j= 1,...,m) of (DΩ1 and on the components Гj (j=k 1,…,m) of of DΩ2 are considered such that DΩl=U^kj=lГj and DΩ2= U^m=k 1Гj and where the coefficients γj(j=1,...,m) are piecewise smooth positive functions. Some applications of θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained. 相似文献
282.
In this paper we show that the weakly -Engel conditions are closely related to the existance of normal -complements; while the -Engel conditions are closely related to the -nilpotent groups.AMS Subject Classification (2000): 20D20 相似文献
283.
Sujit K. Bose 《Proceedings Mathematical Sciences》2001,111(3):365-370
We consider here small flexural vibrations of an Euler-Bernoulli beam with a lumped mass at one end subject to viscous damping
force while the other end is free and the system is set to motion with initial displacementy
0(x) and initial velocityy
1 (x). By investigating the evolution of the motion by Laplace transform, it is proved (in dimensionless units of length and time)
that
, wheret
0 may be sufficiently large, provided that {y
0,y
1} satisfy very general restrictions stated in the concluding theorem. This supplies the restrictions for uniform exponential
energy decay for stabilization of the beam considered in a recent paper. 相似文献
284.
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
285.
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
286.
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
287.
J. Ben Rosen Haesun Park John Glick Lei Zhang 《Computational Optimization and Applications》2000,17(2-3):329-341
It has been known for many years that a robust solution to an overdetermined system of linear equations Ax b is obtained by minimizing the L1 norm of the residual error. A correct solution x to the linear system can often be obtained in this way, in spite of large errors (outliers) in some elements of the (m × n) matrix A and the data vector b. This is in contrast to a least squares solution, where even one large error will typically cause a large error in x. In this paper we give necessary and sufficient conditions that the correct solution is obtained when there are some errors in A and b. Based on the sufficient condition, it is shown that if k rows of [A
b] contain large errors, the correct solution is guaranteed if (m – n)/n 2k/, where > 0, is a lower bound of singular values related to A. Since m typically represents the number of measurements, this inequality shows how many data points are needed to guarantee a correct solution in the presence of large errors in some of the data. This inequality is, in fact, an upper bound, and computational results are presented, which show that the correct solution will be obtained, with high probability, for much smaller values of m – n. 相似文献
288.
José M. Arrieta Alexandre N. Carvalho 《Transactions of the American Mathematical Society》2000,352(1):285-310
We prove a local existence and uniqueness theorem for abstract parabolic problems of the type when the nonlinearity satisfies certain critical conditions. We apply this abstract result to the Navier-Stokes and heat equations.
289.
Beghin Luisa Knopova Viktoria P. Leonenko Nikolai N. Orsingher Enzo 《Journal of statistical physics》2000,99(3-4):769-781
We analyze the asymptotic behavior of the rescaled solution to the linear Korteweg–de Vries equation when the initial conditions are supposed to be random and weakly dependent. By means of the method of moments we prove the Gaussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat-type equation. 相似文献
290.
In order to understand the rise of runaway solutions in the radiation reaction problem a mechanical model is used. An alternative
demonstration of Daboul’s theorem, through Hurwitz’s criterion, is given. The origin of runaway solutions in electrodynamics
is discussed. They arise when the particle has a negative mechanical mass or when approximations are used in the equation
of motion. In the 1-dimensional mechanical model an exact and linear equation of motion for the particle is obtained, the
corresponding exact solution is again runaway when the mechanical mass is negative. The exact solution is not runaway when
the mechanical mass is positive. However, the use of approximations leads to an equation of motion which has runaway solutions.
It is exhibited that the use of approximations in the 3-dimensional mechanical model is completely necessary because the general
equation of motion for the particle is non-linear. The analysis of this case proceeds in a very similar way to the one carried
out in electrodynamics. This means that the number of dimensions also plays an important role in the analysis. 相似文献