9,669 research outputs found
On the existence threshold for positive solutions of p-laplacian equations with a concave-convex nonlinearity
We study the following boundary value problem with a concave-convex
nonlinearity: \begin{equation*} \left\{ \begin{array}{r c l l} -\Delta_p u & =
& \Lambda\,u^{q-1}+ u^{r-1} & \textrm{in }\Omega, \\ u & = & 0 & \textrm{on
}\partial\Omega. \end{array}\right. \end{equation*} Here is a bounded domain and . It is well known that
there exists a number such that the problem admits at least
two positive solutions for , at least one positive
solution for , and no positive solution for . We show that
where is the first eigenvalue of the p-laplacian. It is worth
noticing that is the threshold for existence/nonexistence of
positive solutions to the above problem in the limit case
Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption
Uniqueness and existence of solutions in the BVt(Q) space to a doubly nonlinear parabolic problem
In this paper we present some results on the uniqueness and existence of a class of weak solutions (the so called BV solutions) of the Cauchy-Dirichlet problem associated to the doubly nonlinear diffusion equation
b(u)_t-\operatorname{div}(|\nabla u-k(b(u))\boldkey{e}|^{p-2}(\nabla u-k(b(u))\boldkey{e})) +g(x,u) = f(t,x).
This problem arises in the study of some turbulent regimes: flows of incompressible turbulent fluids through porous media, gases flowing in pipelines, etc. The solvability of this problem is established in the space. We prove some comparison properties (implying uniqueness) when the set of jumping points of the BV solution has -dimensional null measure and suitable additional conditions as, for instance, locally Lipschitz. The existence of this type of weak solution is based on suitable uniform estimates of the BV norm of an approximated solution
Understanding chemical evolution in resolved galaxies -- I The local star fraction-metallicity relation
This work studies the relation between gas-phase oxygen abundance and
stellar-to-gas fraction in nearby galaxies. We first derive the theoretical
prediction, and argue that this relation is fundamental, in the sense that it
must be verified regardless of the details of the gas accretion and star
formation histories. Moreover, it should hold on "local" scales, i.e. in
regions of the order of 1 kpc. These predictions are then compared with a set
of spectroscopic observations, including both integrated and resolved data.
Although the results depend somewhat on the adopted metallicity calibration,
observed galaxies are consistent with the predicted relation, imposing tight
constraints on the mass-loading factor of (enriched) galactic winds. The
proposed parametrization of the star fraction-metallicity relation is able to
describe the observed dependence of the oxygen abundance on gas mass at fixed
stellar mass. However, the "local" mass-metallicity relation also depends on
the relation between stellar and gas surface densities.Comment: 10 pages, 4 figures. Matches accepted version (significant typo
corrected
Astrophysical parameters and orbital solution of the peculiar X-ray transient IGR J00370+6122
BD+6073 is the optical counterpart of the X-ray source IGR J00370+6122, a
probable accretion-powered X-ray pulsar. The X-ray light curve of this binary
system shows clear periodicity at 15.7 d, which has been interpreted as
repeated outbursts around the periastron of an eccentric orbit. We obtained
high-resolution spectra of BD+6073 at different epochs. We used the FASTWind
code to generate a stellar atmosphere model to fit the observed spectrum and
obtain physical magnitudes. The synthetic spectrum was used as a template for
cross-correlation with the observed spectra to measure radial velocities. The
radial velocity curve provided an orbital solution for the system. We have also
analysed the RXTE/ASM and Swift/BAT light curves to confirm the stability of
the periodicity. BD +6073 is a BN0.7 Ib low-luminosity supergiant located at an
approximate distance of 3.1 kpc, in the CasOB4 association. We derive
Teff=24000 K and log gc=3.0, and chemical abundances consistent with a
moderately high level of evolution. The spectroscopic and evolutionary masses
are consistent at the 1 sigma level with a mass of 15 solar masses. The
recurrence time of the X-ray flares is the orbital period of the system. The NS
is in a high eccentricity (e=0.56) orbit, and the X-ray emission is strongly
peaked around orbital phase 0.2, though the observations are consistent with
some level of X-ray activity happening at all orbital phases. The X-ray
behaviour of IGR J00370+6122 is reminiscent of intermediate SFXTs, though its
peak luminosity is rather low. The orbit is somewhat wider than those of
classical persistent supergiant X-ray binaries, which, combined with the low
luminosity of the mass donor, explains the low X-ray luminosity. IGR
J00370+6122 will likely evolve towards a persistent supergiant system,
highlighting the evolutionary connection between different classes of
wind-accreting X-ray sources.Comment: Accepted for publication in A&
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