247 research outputs found
Maximal -regularity for stochastic evolution equations
We prove maximal -regularity for the stochastic evolution equation
\{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t),
\qquad t\in [0,T],
U(0) & = u_0, {aligned}. under the assumption that is a sectorial
operator with a bounded -calculus of angle less than on
a space . The driving process is a cylindrical
Brownian motion in an abstract Hilbert space . For and
and initial conditions in the real interpolation space
\XAp we prove existence of unique strong solution with trajectories in
L^p(0,T;\Dom(A))\cap C([0,T];\XAp), provided the non-linearities
F:[0,T]\times \Dom(A)\to L^q(\mathcal{O},\mu) and B:[0,T]\times \Dom(A) \to
\g(H,\Dom(A^{\frac12})) are of linear growth and Lipschitz continuous in their
second variables with small enough Lipschitz constants. Extensions to the case
where is an adapted operator-valued process are considered as well.
Various applications to stochastic partial differential equations are worked
out in detail. These include higher-order and time-dependent parabolic
equations and the Navier-Stokes equation on a smooth bounded domain
\OO\subseteq \R^d with . For the latter, the existence of a unique
strong local solution with values in (H^{1,q}(\OO))^d is shown.Comment: Accepted for publication in SIAM Journal on Mathematical Analysi
The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth
In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible
A variational approach to strongly damped wave equations
We discuss a Hilbert space method that allows to prove analytical
well-posedness of a class of linear strongly damped wave equations. The main
technical tool is a perturbation lemma for sesquilinear forms, which seems to
be new. In most common linear cases we can furthermore apply a recent result
due to Crouzeix--Haase, thus extending several known results and obtaining
optimal analyticity angle.Comment: This is an extended version of an article appeared in
\emph{Functional Analysis and Evolution Equations -- The G\"unter Lumer
Volume}, edited by H. Amann et al., Birkh\"auser, Basel, 2008. In the latest
submission to arXiv only some typos have been fixe
Stresses in silos: Comparison between theoretical models and new experiments
We present precise and reproducible mean pressure measurements at the bottom
of a cylindrical granular column. If a constant overload is added, the pressure
is linear in overload and nonmonotonic in the column height. The results are
{\em quantitatively} consistent with a local, linear relation between stress
components, as was recently proposed by some of us. They contradict the
simplest classical (Janssen) approximation, and may pose a rather severe test
of competing models.Comment: 4 pages, 2 figures, final version to appear in Phys. Rev. Let
Disorder-induced trapping versus Anderson localization in Bose-Einstein condensates expanding in disordered potentials
We theoretically investigate the localization of an expanding Bose-Einstein
condensate with repulsive atom-atom interactions in a disordered potential. We
focus on the regime where the initial inter-atomic interactions dominate over
the kinetic energy and the disorder. At equilibrium in a trapping potential and
for small disorder, the condensate shows a Thomas-Fermi shape modified by the
disorder. When the condensate is released from the trap, a strong suppression
of the expansion is obtained in contrast to the situation in a periodic
potential with similar characteristics. This effect crucially depends on both
the momentum distribution of the expanding BEC and the strength of the
disorder. For strong disorder, the suppression of the expansion results from
the fragmentation of the core of the condensate and from classical reflections
from large modulations of the disordered potential in the tails of the
condensate. We identify the corresponding disorder-induced trapping scenario
for which large atom-atom interactions and strong reflections from single
modulations of the disordered potential play central roles. For weak disorder,
the suppression of the expansion signals the onset of Anderson localization,
which is due to multiple scattering from the modulations of the disordered
potential. We compute analytically the localized density profile of the
condensate and show that the localization crucially depends on the correlation
function of the disorder. In particular, for speckle potentials the long-range
correlations induce an effective mobility edge in 1D finite systems. Numerical
calculations performed in the mean-field approximation support our analysis for
both strong and weak disorder.Comment: New Journal of Physics; focus issue "Quantum Correlations in Tailored
Matter - Common perspectives of mesoscopic systems and quantum gases"; 30
pages, 10 figure
Supergravity p-branes revisited: extra parameters, uniqueness, and topological censorship
We perform a complete integration of the Einstein-dilaton-antisymmetric form
action describing black p-branes in arbitrary dimensions assuming the
transverse space to be homogeneous and possessing spherical, toroidal or
hyperbolic topology. The generic solution contains eight parameters satisfying
one constraint. Asymptotically flat solutions form a five-parametric subspace,
while conditions of regularity of the non-degenerate event horizon further
restrict this number to three, which can be related to the mass and the charge
densities and the asymptotic value of the dilaton. In the case of a degenerate
horizon, this number is reduced by one. Our derivation constitutes a
constructive proof of the uniqueness theorem for -branes with the
homogeneous transverse space. No asymptotically flat solutions with toroidal or
hyperbolic transverse space within the considered class are shown to exist,
which result can be viewed as a demonstration of the topological censorship for
p-branes. From our considerations it follows, in particular, that some
previously discussed p-brane-like solutions with extra parameters do not
satisfy the standard conditions of asymptotic flatness and absence of naked
singularities. We also explore the same system in presence of a cosmological
constant, and derive a complete analytic solution for higher-dimensional
charged topological black holes, thus proving their uniqueness.Comment: Revtex4, no figure
Steady states in a structured epidemic model with Wentzell boundary condition
We introduce a nonlinear structured population model with diffusion in the
state space. Individuals are structured with respect to a continuous variable
which represents a pathogen load. The class of uninfected individuals
constitutes a special compartment that carries mass, hence the model is
equipped with generalized Wentzell (or dynamic) boundary conditions. Our model
is intended to describe the spread of infection of a vertically transmitted
disease, for example Wolbachia in a mosquito population. Therefore the
(infinite dimensional) nonlinearity arises in the recruitment term. First we
establish global existence of solutions and the Principle of Linearised
Stability for our model. Then, in our main result, we formulate simple
conditions, which guarantee the existence of non-trivial steady states of the
model. Our method utilizes an operator theoretic framework combined with a
fixed point approach. Finally, in the last section we establish a sufficient
condition for the local asymptotic stability of the positive steady state
Measurement of the p-pbar -> Wgamma + X cross section at sqrt(s) = 1.96 TeV and WWgamma anomalous coupling limits
The WWgamma triple gauge boson coupling parameters are studied using p-pbar
-> l nu gamma + X (l = e,mu) events at sqrt(s) = 1.96 TeV. The data were
collected with the DO detector from an integrated luminosity of 162 pb^{-1}
delivered by the Fermilab Tevatron Collider. The cross section times branching
fraction for p-pbar -> W(gamma) + X -> l nu gamma + X with E_T^{gamma} > 8 GeV
and Delta R_{l gamma} > 0.7 is 14.8 +/- 1.6 (stat) +/- 1.0 (syst) +/- 1.0 (lum)
pb. The one-dimensional 95% confidence level limits on anomalous couplings are
-0.88 < Delta kappa_{gamma} < 0.96 and -0.20 < lambda_{gamma} < 0.20.Comment: Submitted to Phys. Rev. D Rapid Communication
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