共查询到20条相似文献,搜索用时 15 毫秒
1.
Mourad Bellassoued 《Communications in Mathematical Physics》2000,215(2):375-408
We study resonances (scattering poles) associated to the elasticity operator in the exterior of an arbitrary obstacle with
Neumann or Dirichlet boundary conditions. We prove that there exists an exponentially small neighborhood of the real axis
free of resonances. Consequently we prove that for regular data, the energy for the elastic wave equation decays at least
as fast as the inverse of the logarithm of time. According to Stefanov–Vodev ([SV1, SV2]), our results are optimal in the
case of a Neumann boundary condition, even when the obstacle is a ball of ℝ3. The main difference between our case and the case of the scalar Laplacian (see Burq [Bu]) is the phenomenon of Rayleigh
surface waves, which are connected to the failure of the Lopatinskii condition.
Received: 22 February 2000 / Accepted: 28 June 2000 相似文献
2.
Emmanuel Schenck 《Communications in Mathematical Physics》2010,300(2):375-410
We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature.
This result holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic
flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay
is governed by the imaginary part of a finite number of eigenvalues close to the real axis. 相似文献
3.
F. Finster N. Kamran J. Smoller S.-T. Yau 《Communications in Mathematical Physics》2006,264(2):465-503
We consider the Cauchy problem for the massless scalar wave equation in the Kerr geometry for smooth initial data compactly
supported outside the event horizon. We prove that the solutions decay in time in L
∞
loc. The proof is based on a representation of the solution as an infinite sum over the angular momentum modes, each of which
is an integral of the energy variable ω on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation
of variables.
Research supported in part by the Deutsche Forschungsgemeinschaft.
Research supported by NSERC grant #RGPIN 105490-2004.
Research supported in part by the NSF, Grant No. DMS-010-3998.
Research supported in part by the NSF, Grant No. 33-585-7510-2-30.
An erratum to this article is available at . 相似文献
4.
5.
We prove sharp pointwise t
−3 decay for scalar linear perturbations of a Schwarzschild black hole without symmetry assumptions on the data. We also consider
electromagnetic and gravitational perturbations for which we obtain decay rates t
−4, and t
−6, respectively. We proceed by decomposition into angular momentum ℓ and summation of the decay estimates on the Regge-Wheeler
equation for fixed ℓ. We encounter a dichotomy: the decay law in time is entirely determined by the asymptotic behavior of the Regge-Wheeler potential
in the far field, whereas the growth of the constants in ℓ is dictated by the behavior of the Regge-Wheeler potential in a small neighborhood around its maximum. In other words, the
tails are controlled by small energies, whereas the number of angular derivatives needed on the data is determined by energies
close to the top of the Regge-Wheeler potential. This dichotomy corresponds to the well-known principle that for initial times
the decay reflects the presence of complex resonances generated by the potential maximum, whereas for later times the tails
are determined by the far field. However, we do not invoke complex resonances at all, but rely instead on semiclassical Sigal-Soffer
type propagation estimates based on a Mourre bound near the top energy. 相似文献
6.
7.
Serge Alinhac 《Communications in Mathematical Physics》2009,288(1):199-224
We consider the wave equations associated to metrics close to the Schwarzschild metric. We investigate spacelike energy multipliers
likely to yield local decay of solutions to these wave equations, in the spirit of Morawetz. For rotationally invariant metrics,
we obtain multipliers giving a control of the solutions having finitely many vanishing spherical harmonics. The structure
of these multipliers is closely related to the photosphere of the metric. For Kerr metrics, in contrast, we display a region,
which we call the intersphere region, where no energy inequality with the required properties can exist. 相似文献
8.
波动方程深度偏移的局部裂步Fourier传播算子 总被引:2,自引:1,他引:1
针对裂步Fourier传播算子在速度强横向变化介质中的不足,将算子的框架展开方法应用于Fourier传播算子中的相移算子,提出了一种波场传播的局部裂步Fourier传播算子,并把它应用于波动方程叠前深度偏移成像.这个局部裂步Fourier传播算子是由相空间(空间-波数)-频率域的相移算子和空间-频率域的窗口时移算子两部分组成.与波数-频率域的空间全局性相移算子不同,相空间-频率域的相移算子具有很好的空间局部性.通过在国际标准的SEG-EAGE二维盐丘模型的波动方程叠前深度偏移成像数值试验,证明局部Fourier传播算子不仅具有很好的稳定性,而且还特别适用于速度强横向变化介质. 相似文献
9.
We study the existence and the uniqueness of stationary solutions for discrete velocity models of the Boltzmann equation in
the first half space. We obtain a sufficient condition that guarantees the existence and the uniqueness of solutions connecting
the given boundary data and the Maxwellian state at a spatially asymptotic point. First, a sufficient condition is obtained
for the linearized system. Then this result as well as the contraction mapping principle is applied to prove the existence
theorem for the nonlinear equation. Also, we show that the stationary wave approaches the Maxwellian state exponentially at
a spatially asymptotic point.
We also discuss some concrete models of Boltzmann type as an application of our general theory. Here, it turns out that our
sufficient condition is general enough to cover many concrete models.
Received: 7 December 1998 / Accepted: 27 April 1999 相似文献
10.
For convex co-compact hyperbolic quotients , we analyze the long-time asymptotic of the solution of the wave equation u(t) with smooth compactly supported initial data f = (f
0, f
1). We show that, if the Hausdorff dimension δ of the limit set is less than n/2, then where and . We explain, in terms of conformal theory of the conformal infinity of X, the special cases , where the leading asymptotic term vanishes. In a second part, we show for all the existence of an infinite number of resonances (and thus zeros of Selberg zeta function) in the strip . As a byproduct we obtain a lower bound on the remainder R(t) for generic initial data f. 相似文献
11.
12.
Using the property of the simplest invariant built from the covariant derivatives of the curvature tensor to change sign on the Schwarzschild horizon, and the relativistic quadratic geodesic deviation equation to express the invariant in terms of locally measurable quantities, viz., separation, relative velocity and acceleration of test particles, a scheme is presented which can, in principle, be used by an imaginary observer to detect by local measurements the passage through the event horizon in the Schwarzschild spacetime. 相似文献
13.
Eric Paturel 《Communications in Mathematical Physics》2000,213(2):249-266
In this paper, we prove the existence of infinitely many solutions of a stationary nonlinear Dirac equation on the Schwarzschild
metric, outside a massive ball. These solutions are the critical points of a strongly indefinite functional. Thanks to a concavity
property, we are able to construct a reduced functional, which is no longer strongly indefinite. We find critical points of
this new functional using the Symmetric Mountain Pass Lemma. Note that, as A. Bachelot-Motet conjectured, these solutions
vanish as the radius of the massive ball tends to the horizon radius of the metric.
Received: 2 August 1999 / Accepted: 14 February 2000 相似文献
14.
We examine the influence of relativistic gravitational effects and rotation of a central body on the structure of the quasidiscrete energy spectrum of a spinless particle in the field of Schwarzschild and Kerr black holes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp 71–76, October, 1988. 相似文献
15.
Derivation of Dirac's Equation from the Evans Wave Equation 总被引:1,自引:0,他引:1
M. W. Evans 《Foundations of Physics Letters》2004,17(2):149-166
The Evans wave equation [1] of general relativity is expressed in spinor form, thus producing the Dirac equation in general relativity. The Dirac equation in special relativity is recovered in the limit of Euclidean or flat spacetime. By deriving the Dirac equation from the Evans equation it is demonstrated that the former originates in a novel metric compatibility condition, a geometrical constraint on the metric vector qused to define the Einstein metric tensor. Contrary to some claims by Ryder, it is shown that the Dirac equation cannot be deduced unequivocally from a Lorentz boost in special relativity. It is shown that the usually accepted method in Clifford algebra and special relativity of equating the outer product of two Pauli spinors to a three-vector in the Pauli basis leads to the paradoxical result X = Y = Z = 0. The method devised in this paper for deriving the Dirac equation from the Evans equation does not use this paradoxical result. 相似文献
16.
James D.E. Grant Eberhard Mayerhofer Roland Steinbauer 《Communications in Mathematical Physics》2009,285(2):399-420
We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics
in a suitable space of generalised functions. 相似文献
17.
Pedro Isaza Felipe Linares Gustavo Ponce 《Communications in Mathematical Physics》2013,324(1):129-146
We prove special decay properties of solutions to the initial value problem associated to the k-generalized Korteweg-de Vries equation. These are related with persistence properties of the solution flow in weighted Sobolev spaces and with sharp unique continuation properties of solutions to this equation. As an application of our method we also obtain results concerning the decay behavior of perturbations of the traveling wave solutions as well as results for solutions corresponding to special data. 相似文献
18.
Using Leaver's continue fraction and time domain method, we investigate the wave dynamics of phantom scalar perturbation in the background of Schwarzschild black hole. We find that the presence of the negative kinetic energy terms modifies the standard results in quasinormal spectrums and late-time behaviors of the scalar perturbations. The phantom scalar perturbation in the late-time evolution will grow with an exponential rate. 相似文献
19.
For nonsoft potential collision kernels with angular cutoff, we prove that under the initial condition f
0(v)(1+|v|2+|logf
0(v)|)L
1(R
3), the classical formal entropy identity holds for all nonnegative solutions of the spatially homogeneous Boltzmann equation in the class L
([0, ); L
1
2(R
3))C
1([0, ); L
1(R
3)) [where L
1
s
(R
3)={ff(v)(1+|v|2)
s/2L
1(R
3)}], and in this class, the nonincrease of energy always implies the conservation of energy and therefore the solutions obtained all conserve energy. Moreover, for hard potentials and the hard-sphere model, a local stability result for conservative solutions (i.e., satisfying the conservation of mass, momentum, and energy) is obtained. As an application of the local stability, a sufficient and necessary condition on the initial data f
0 such that the conservative solutions f belong to L
1
loc([0, ); L
1
2+
(R
3)) is also given. 相似文献
20.
The effective Lagrangian and the zero-point (or Casimir) energy is calculated from the zeta-function which is obtained by the heat kernel method using the expansion of (Bormann and Antonsen, 1995). Calculated this way this unavoidable energy contribution is automatically regularised and ready for further investigation. Interesting observations include a large energy contribution (from scalar field and fermionic zero-point fluctuations) that is non-zero as the mass goes to zero, perhaps indicating a topological origin. Also, plots of the contribution of gauge boson fields to the zero-point energy, as a function of radial distance (gravitational field strength) and the size of the gauge boson coupling (gauge field strength) shows great variation, notably the occurrence of resonances. 相似文献