2,768 research outputs found
An overdetermined problem for the anisotropic capacity
We consider an overdetermined problem for the Finsler Laplacian in the
exterior of a convex domain in , establishing a symmetry result
for the anisotropic capacitary potential. Our result extends the one of W.
Reichel [Arch. Rational Mech. Anal. 137 (1997)], where the usual Newtonian
capacity is considered, giving rise to an overdetermined problem for the
standard Laplace equation. Here, we replace the usual Euclidean norm of the
gradient with an arbitrary norm . The resulting symmetry of the solution is
that of the so-called Wulff shape (a ball in the dual norm )
The inefficiency of satellite accretion in forming extended star clusters
The distinction between globular clusters and dwarf galaxies has been
progressively blurred by the recent discoveries of several extended star
clusters, with size (20-30 pc) and luminosity (-6 < Mv < -2) comparable to the
one of faint dwarf spheroidals. In order to explain their sparse structure, it
has been suggested that they formed as star clusters in dwarf galaxy satellites
that later accreted onto the Milky Way. If these clusters form in the centre of
dwarf galaxies, they evolve in a tidally-compressive environment where the
contribution of the tides to the virial balance can become significant, and
lead to a super-virial state and subsequent expansion of the cluster, once
removed. Using N-body simulations, we show that a cluster formed in such an
extreme environment undergoes a sizable expansion, during the drastic variation
of the external tidal field due to the accretion process. However, we show that
the expansion due to the removal of the compressive tides is not enough to
explain the observed extended structure, since the stellar systems resulting
from this process are always more compact than the corresponding clusters that
expand in isolation due to two-body relaxation. We conclude that an accreted
origin of extended globular clusters is unlikely to explain their large spatial
extent, and rather favor the hypothesis that such clusters are already extended
at the stage of their formation.Comment: 5 pages, 4 figures, 1 table. Accepted for publication in MNRAS
Letter
Stability of solutions for hyperbolic systems with coinciding shocks and rarefactions
We consider a hyperbolic system of conservation laws u_t + f(u)_x = 0 and
u(0,\cdot) = u_0, where each characteristic field is either linearly degenerate
or genuinely nonlinear. Under the assumption of coinciding shock and
rarefaction curves and the existence of a set of Riemann coordinates , we
prove that there exists a semigroup of solutions ,
defined on initial data . The semigroup is
continuous w.r.t. time and the initial data in the
topology. Moreover is unique and its trajectories are obtained as
limits of wave front tracking approximations.Comment: 19 pages, 13 figure
- …