共查询到20条相似文献,搜索用时 31 毫秒
1.
Demetrios Christodoulou 《Communications in Mathematical Physics》1986,105(3):337-361
In this paper we begin the study of the global initial value problem for Einstein's equations in the spherically symmetric case with a massless scalar field as the material model. We reduce the problem to a single nonlinear evolution equation. Taking as initial hypersurface a future light cone with vertex at the center of symmetry, we prove, the local, in retarded time, existence and global uniqueness of classical solutions. We also prove that if the initial data is sufficiently small there exists a global classical solution which disperses in the infinite future.Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University 相似文献
2.
流动数值模拟中一种并行自适应有限元算法 总被引:1,自引:0,他引:1
给出了一种流动数值模拟中的基于误差估算的并行网格自适应有限元算法.首先,以初网格上获得的当地事后误差估算值为权,应用递归谱对剖分方法划分初网格,使各子域上总体误差近似相等,以解决负载平衡问题.然后以误差值为判据对各子域内网格进行独立的自适应处理.最后应用基于粘接元的区域分裂法在非匹配的网格上求解N-S方程.区域分裂情形下N-S方程有限元解的误差估算则是广义Stokes问题误差估算方法的推广.为验证方法的可靠性,给出了不可压流经典算例的数值结果. 相似文献
3.
We introduce a generalized isospectral problem for global conservative multi-peakon solutions of the Camassa–Holm equation. Utilizing the solution of the indefinite moment problem given by M. G. Krein and H. Langer, we show that the conservative Camassa–Holm equation is integrable by the inverse spectral transform in the multi-peakon case. 相似文献
4.
In this paper, we present the theory of constructing optimal generalized helical-wave coupling dynamical systems. Applying the helical-wave decomposition method to Navier-Stokes equations, we derive a pair of coupling dynamical systems based on optimal generalized helical-wave bases. Then with the method of multi-scale global optimization based on coarse graining analysis, a set of global optimal generalized helical-wave bases is obtained. Optimal generalized helical-wave bases retain the good properties of classical helical-wave bases. Moreover, they are optimal for the dynamical systems of Navier-Stokes equations, and suitable for complex physical and geometric boundary conditions. Then we find that the optimal generalized helical-wave vortexes fitted by a finite number of optimal generalized helical-wave bases can be used as the fundamental elements of turbulence, and have important significance for studying physical properties of complex flows and turbulent vortex structures in a deeper level. 相似文献
5.
In this paper, we consider the global well-posedness and long-time dynamics for the three-dimensional viscous primitive equations
describing the large-scale oceanic motion under a random forcing, which is an additive white in time noise. We firstly prove
the existence and uniqueness of global strong solutions to the initial boundary value problem for the stochastic primitive
equations. Subsequently, by studying the asymptotic behavior of strong solutions, we obtain the existence of random attractors
for the corresponding random dynamical system. 相似文献
6.
In the present paper we study the evolution of a system of hard disks moving in the plane with a finite number of velocities as in the framework of a discrete velocity model of the Enskog equation, proposed in previous papers. Starting from the BBGKY hierarchy of such a system we give existence and uniqueness results for the initial value problem in suitable Banach spaces. In particular, the main result presented is the global in time weak solution to the BBGKY hierarchy for local equilibrium initial data, in the thermodynamic limit. 相似文献
7.
Nosikov I. A. Padokhin A. M. Krasheninnikov I. V. Klimenko M. V. Bessarab P. F. 《Radiophysics and Quantum Electronics》2022,64(8-9):605-617
Radiophysics and Quantum Electronics - We apply two promising approaches, namely, the shooting method based on global optimization and the generalized force method, to the problem of point-to-point... 相似文献
8.
Jonatan Lenells 《Physica D: Nonlinear Phenomena》2011,240(6):512-525
We consider initial-boundary value problems for the derivative nonlinear Schrödinger (DNLS) equation on the half-line x>0. In a previous work, we showed that the solution q(x,t) can be expressed in terms of the solution of a Riemann-Hilbert problem with jump condition specified by the initial and boundary values of q(x,t). However, for a well-posed problem, only part of the boundary values can be prescribed; the remaining boundary data cannot be independently specified, but are determined by the so-called global relation. In general, an effective solution of the problem therefore requires solving the global relation. Here, we present the solution of the global relation in terms of the solution of a system of nonlinear integral equations. This also provides a construction of the Dirichlet-to-Neumann map for the DNLS equation on the half-line. 相似文献
9.
Large-Time Behavior of Solutions to the Equations of
a One-Dimensional Viscous Polytropic Ideal Gas in Unbounded Domains 总被引:2,自引:0,他引:2
Song Jiang 《Communications in Mathematical Physics》1999,200(1):181-193
The large-time behavior of solutions to the initial and initial boundary value problems for a one-dimensional viscous polytropic
ideal gas in unbounded domains is investigated. Using a special cut-off function to localize the problem, we derive a local
representation for the specific volume. With the help of the local representation, and certain new estimates for the temperature
and the stress, and the weighted energy estimates, we prove that in any bounded interval, the specific volume is pointwise
bounded from below and above for all t≥ 0 and a generalized solution is convergent as time goes to infinity.
Received: 21 July 1997/ Accepted: 21 June 1998 相似文献
10.
Yeong-Jeu Sun 《Physics letters. A》2010,374(7):933-1834
In this Letter, the generalized Lorenz chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a simple observer for the generalized Lorenz chaotic system is developed to guarantee the global exponential stability of the resulting error system. Moreover, the guaranteed exponential convergence rate can be correctly estimated. Finally, a numerical example is given to show the effectiveness of the obtained result. 相似文献
11.
S. Yu. Dobrokhotov B. Tirozzi C. A. Vargas 《Russian Journal of Mathematical Physics》2009,16(2):228-245
We study the behavior of the wave part of asymptotic solutions to the Cauchy problem for linearized shallow water equations
with initial perturbations localized near the origin. The global representation for these solutions based on the generalized
Maslov canonical operator was given earlier. The asymptotic solutions are also localized in the neighborhood of certain curves
(fronts). The simplification of general formulas and the behavior of asymptotic solutions in a neighborhood of the regular
part of fronts was also given earlier. Here the behavior of asymptotic solutions in a neighborhood of the focal point of the
fronts is discussed in detail and the proof of formulas announced earlier for the wave equation is given. This paper can be
regarded as a continuation of the paper in Russiian Journal of Mathematical Physics 15 (2), 192–221 (2008).
In memoriam V.A. Borovikov 相似文献
12.
Using the method of radio sounding of the mid-latitude ionosphere by the satellite signals, we study the multifractal structure
of small-scale ionospheric turbulence during a solar eclipse. The measured multipower and generalized multifractal spectra
of small-scale ionospheric turbulence at the initial and closing stages of the eclipse turn out to be almost identical on
the space radio paths with different orientations. This is indicative of a sufficiently high stability of the nonuniform spatio-temporal
distribution of small-scale fluctuations of the ionospheric electron number density under conditions of geophysical disturbances
due to global physical processes in the ionospheric plasma during a solar eclipse.
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 4, pp. 302–306, April 2009. 相似文献
13.
Buckling of an elastic linkage under general loading is investigated. We show that buckling is related to an initial value problem, which is always a conservative, area-preserving mapping, even if the original static problem is nonconservative. In some special cases, we construct the global bifurcation diagrams, and argue that their complicated structure is a consequence of spatial chaos. We characterize spatial chaos by the associated initial value problem's topological entropy, which turns out to be related to the number of buckled configurations. 相似文献
14.
Ting Zhang 《Communications in Mathematical Physics》2009,287(1):211-224
In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (ANS). We prove the global wellposedness for ANS provided the initial horizontal data are sufficient small in the scaling invariant Besov-Sobolev type space . In particular, the result implies the global wellposedness of ANS with large initial vertical velocity. 相似文献
15.
We give a global picture of the normalized Ricci flow on generalized flag manifolds with two or three isotropy summands. The normalized Ricci flow for these spaces reduces to a parameter-dependent system of two or three ordinary differential equations, respectively. Here, we present a qualitative study of these systems’ global phase portrait, which uses techniques of dynamical systems theory. This study allows us to draw conclusions about the existence and the analytical form of invariant Einstein metrics on such manifolds and seems to offer a better insight to the classification problem of invariant Einstein metrics on compact homogeneous spaces. 相似文献
16.
In this paper, we investigate a class of stochastic quasilinear parabolic initial boundary value problems with nonstandard growth in the functional setting of generalized Sobolev spaces. The deterministic version of the equation was first introduced and studied by Samokhin in [45] as a generalized model for polytropic filtration. We establish an existence result of weak probabilistic solutions when the forcing terms do not satisfy Lipschitz conditions. Under the Lipschitz property of the forcing terms, we obtain the uniqueness of weak probabilistic solutions. Combining the uniqueness and the famous Yamada–Watanabe result, we prove the existence of a unique strong probabilistic solution of the problem. 相似文献
17.
Matthias Kotschote 《Communications in Mathematical Physics》2014,328(2):809-847
In this paper we establish global existence and uniqueness of strong solutions to the non-isothermal compressible Navier–Stokes equations in bounded domains. The initial data have to be near equilibria that may be non-constant due to considering large external forces. We are able to show exponential stability of equilibria in the phase space and, above all, to study the problem in Eulerian coordinates. The latter seems to be a novelty, since in works by other authors, global strong L p -solutions have been investigated only in Lagrangian coordinates; Eulerian coordinates are even declared as impossible to deal with. The proof is based on a careful derivation and study of the associated linear problem. 相似文献
18.
Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the
eigenfunctions of certain Schr?dinger operators for Calogero-Sutherland-type quantum systems. For the generalized Hermite
and Laguerre polynomials the multidimensional analogues of many classical results regarding generating functions, differentiation
and integration formulas, recurrence relations and summation theorems are obtained. We use this and related theory to evaluate
the global limit of the ground state density, obtaining in the Hermite case the Wigner semi-circle law, and to give an explicit
solution for an initial value problem in the Hermite and Laguerre case.
Received: 16 August 1996 / Accepted: 21 January 1997 相似文献
19.
On the Generalized Thermoelasticity Problem for an Infinite Fibre-Reinforced Thick Plate under Initial Stress
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Ahmed E. Abouelregal & Ashraf M. Zenkour 《advances in applied mathematics and mechanics.》2014,6(6):783-796
In this paper, the generalized thermoelasticity problem for an infinite
fiber-reinforced transversely-isotropic thick plate subjected to initial
stress is solved. The lower surface of the plate rests on a rigid foundation
and temperature while the upper surface is thermally insulated with prescribed
surface loading. The normal mode analysis is used to obtain the analytical
expressions for the displacements, stresses and temperature distributions.
The problem has been solved analytically using the generalized thermoelasticity
theory of dual-phase-lags. Effect of phase-lags, reinforcement and initial stress
on the field quantities is shown graphically. The results due to the coupled
thermoelasticity theory, Lord and Shulman's theory, and Green and Naghdi's theory
have been derived as limiting cases. The graphs illustrated that the initial stress,
the reinforcement and phase-lags have great effects on the distributions of the field quantities. 相似文献
20.
Gioel Calabrese Jorge Pullin Oscar Reula Olivier Sarbach Manuel Tiglio 《Communications in Mathematical Physics》2003,240(1-2):377-395
In this paper we address the problem of specifying boundary conditions for Einstein's equations when linearized around Minkowski space using the generalized Einstein-Christoffel symmetric hyperbolic system of evolution equations. The boundary conditions we work out guarantee that the constraints are satisfied provided they are satisfied on the initial slice and ensures a well posed initial-boundary value formulation. We consider the case of a manifold with a non-smooth boundary, as is the usual case of the cubic boxes commonly used in numerical relativity. The techniques discussed should be applicable to more general cases, as linearizations around more complicated backgrounds, and may be used to establish well posedness in the full non-linear case. 相似文献