The conformal gravity fit to observed galactic rotation curves requires γ>0. On the other hand, the conventional method for light deflection by galaxies gives a negative contribution to the Schwarzschild value for γ>0, which is contrary to observation. Thus, it is very important that the contribution to bending should in principle be positive, no matter how small its magnitude is. Here we show that the Rindler-Ishak method gives a positive contribution to Schwarzschild deflection for γ>0, as desired. We also obtain the exact local coupling term derived earlier by Sereno. These results indicate that conformal gravity can potentially test well against all astrophysical observations to date

In this paper we study the long-term dynamics of a nonlinear suspension bridge system. The road bed and the main cable are modeled as a nonlinear beam and a vibrating string, respectively, and their coupling is carried out by one-sided springs. First, we scrutinize the set of stationary solutions, which turns out to be nontrivial when the axial load exceeds some critical value. Then, we prove the existence of a bounded global attractor of optimal regularity and we give its characterization in terms of the steady states of the problem.

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This work is focused on the doubly nonlinear equation , whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness . When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load and stiffness . For a general external source , we prove the existence of bounded absorbing sets. When is time-independent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity and its characterization is given in terms of the steady states of the problem.

We present a new analytical solution of the Einstein field equations describing a wormhole shell of zero thickness joining two Lemaître-Tolman-Bondi universes, with no radial accretion. The material on the shell satisfies the energy conditions and, at late times, the shell becomes comoving with the dust-dominated cosmic substratum.

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The Einstein evolution of a dust shell universe with spatial spherical symmetry is analyzed. The implicit and parametric solutions of Tolman-Bondi equations are proposed in order to show its agreement with the rectilinear solutions of Kepler's problem. Finally, a complete systematization of Tolman-Bondi models is obtained through the classical Weierstrass approach.

A model of nonlocal heat transfer at nanoscale in rigid bodies is considered. Depending on the relevance of the particular interaction’s mechanism between the heat carriers and the lateral walls, three different strategies for the setting-up of the boundary conditions are analyzed, and the consequent forms of the basic fields have been obtained, as well. From the physical point of view, the possible influence of those interactions on the unknown fields is pointed out. From the mathematical point of view, instead, the well-posedness of the problem is shown.