Continuity in a parameter of solutions to generic boundary-value problems

We introduce the most general class of linear boundary-value problems for systems of first-order ordinary differential equations whose solutions belong to the complex H\"older space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and $0\leq\alpha\leq1$. The boundary conditions can contain derivatives $y^{(r)}$, with $1\leq r\leq n+1$, of the solution $y$ to the system. For parameter-dependent problems from this class, we obtain constructive criterion under which their solutions are continuous in the normed space $C^{n+1,\alpha}$ with respect to the parameter.Comment: 15 page

Estimation of the Shear Viscosity from 3FD Simulations of Au+Au Collisions at sNN=\sqrt{s_{NN}}= 3.3--39 GeV

An effective shear viscosity in central Au+Au collisions is estimated in the range of incident energies 3.3 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The simulations are performed within a three-fluid model employing three different equations of state with and without the deconfinement transition. In order to estimate this effective viscosity, we consider the entropy produced in the 3FD simulations as if it is generated within the conventional one-fluid viscous hydrodynamics. It is found that the effective viscosity within different considered scenarios is very similar at the expansion stage of the collision: as a function of temperature ($T$) the viscosity-to-entropy ratio behaves as $\eta/s \sim 1/T^4$; as a function of net-baryon density ($n_B$), $\eta/s \sim 1/s$, i.e. it is mainly determined by the density dependence of the entropy density. The above dependencies take place along the dynamical trajectories of Au+Au collisions. At the final stages of the expansion the $\eta/s$ values are ranged from $\sim$0.05 at highest considered energies to $\sim$0.5 at the lowest ones.Comment: 4 pages, 3 figures, to be published in Eur. Phys. Journ.

Entropy Production and Effective Viscosity in Heavy-Ion Collisions

Entropy production and an effective viscosity in central Au+Au collisions are estimated in a wide range of incident energies 3.3 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The simulations are performed within a three-fluid model employing three different equations of state with and without deconfinement transition, which are equally good in reproduction of the momentum-integrated elliptic flow of charged particles in the considered energy range. It is found that more that 80\% entropy is prodused during a short early collision stage which lasts $\sim$1 fm/c at highest considered energies $\sqrt{s_{NN}}\ge$ 20 GeV. The estimated values of the viscosity-to-entropy ratio ($\eta/s$) are approximately the same in all considered scenarios. At final stages of the system expansion they range from $\sim$0.05 at highest considered energies to $\sim$0.5 lowest ones. It is found that the $\eta/s$ ratio decreases with the temperature ($T$) rise approximately as $\sim 1/T^4$ and exhibits a rather weak dependence on the net-baryon density.Comment: 10 pages, 9 figures. Version accepted for publication in the European Physical Journal

High baryon and energy densities achievable in heavy-ion collisions at sNN=\sqrt{s_{NN}}= 39 GeV

Baryon and energy densities, which are reached in central Au+Au collisions at collision energy of $\sqrt{s_{NN}}= 39$ GeV, are estimated within the model of three-fluid dynamics. It is shown that the initial thermalized mean proper baryon and energy densities in a sizable central region approximately are $n_B/n_0 \approx$ 10 and $\varepsilon\approx$ 40 GeV/fm$^3$, respectively. The study indicates that the deconfinement transition at the stage of interpenetration of colliding nuclei makes the system quite opaque. The final fragmentation regions in these collisions are formed not only by primordial fragmentation fireballs, i.e. the baryon-rich matter passed through the interaction region (containing approximately 30\% of the total baryon charge), but also by the baryon-rich regions of the central fireball pushed out to peripheral rapidities by the subsequent almost one-dimensional expansion of the central fireball along the beam direction.Comment: 4 pages, 4 figures, minor corrections, version published in Phys. Rev.

Problem of Bitsadze-Samarskii type for second-order elliptic systems in the plane

For general elliptic equations Bitsadze-Samara has been the subject of numerous studies. In this paper, the problem is considered for functions analytic DouglisyesBelgorod State Universit