Catálogo de publicaciones - libros

We show how the action on two simultaneous effects (a suitable coupling about velocity and temperature and a low range of temperature but upper that the phase changing one) may be responsible of stopping a viscous fluid without any changing phase. Our model involves a system, on an unbounded pipe, given by the planar stationary Navier-Stokes equation perturbed with a sublinear term (,, u) coupled with a stationary (and possibly nonlinear) advection diffusion equation for the temperature .

After proving some results on the existence and uniqueness of weak solutions we apply an energy method to show that the velocity u vanishes for large enough.

We consider the equation= Δ() with 2 ≤ < on a compact Riemannian manifold. We prove that any solution () approaches its (time-independent) mean with the quantitative boundfor any ∊ [2, +∞] and > 0 and the exponents , are shown to be the only possible for a bound of such type. The proof is based upon the connection between logarithmic Sobolev inequalities and decay properties of nonlinear semigroups.

We consider the velocity field () of a Navier-Stokes flow in the whole space.

We give a persistence result in a subspace of (, (1 + ||)), which allows us to fill the gap between previously known results in the weighted- setting and those on the pointwise decay of at infinity.

A -Laplacian flow (1 < < ∞) with nonlocal diffusivity is obtained as an asymptotic limit case of a high thermal conductivity flow described by a coupled system involving the dissipation energy.

We consider the unsteady motion of a drop in another incompressible fluid. On the unknown interface between the liquids, the surface tension is taken into account. Moreover, the coe cient of surface tension depends on the temperature. We study this problem of the thermocapillary convection by M.V. Lagunova and V.A. Solonnikov’s technique developed for a single liquid.

The local existence theorem for the problem is proved in Hölder classes of functions. The proof is based on the fact that the solvability of the problem with a constant coe cient of surface tension was obtain earlier. For a given velocity vector field of the fluids, we arrive at a di raction problem for the heat equation which solvability is established by well-known methods. Existence of a solution to the complete problem is proved by successive approximations.

We present a mathematical model for the phototransduction cascade, taking into account the spatial localization of the different reaction processes. The geometric complexity of the problem (set in the rod outer segment) is simplified by a process of homogenization and concentration of capacity.

We consider the equation= Δ() with 2 ≤ < on a compact Riemannian manifold. We prove that any solution () approaches its (time-independent) mean with the quantitative boundfor any ∊ [2, +∞] and > 0 and the exponents , are shown to be the only possible for a bound of such type. The proof is based upon the connection between logarithmic Sobolev inequalities and decay properties of nonlinear semigroups.

We study the phenomenon of thermally induced mass transport in partially saturated solutions under a thermal gradient, accompanied by deposition of the solid segregated phase on the “cold” boundary. We formulate a one-dimensional model including the displacement of all species (solvent, solute and segregated phase) and we analyze a typical case establishing existence and uniqueness.

We consider a time-dependent problem for a viscous incompressible nonhomogeneous fluid bounded by a free surface on which surface tension forces act. We prove the local in time solvability theorem for this problem in Sobolev function spaces. In the nonhomogeneous model the density of the fluid is unknown. Going over to Lagrange coordinates connected with the velocity vector field, we pass from the free boundary problem to the problem in the fixed boundary domain. Due to the continuity equation, in Lagrange coordinates the density is the same as at the initial moment of time. It gives us the possibility to apply the methods developed by V.A. Solonnikov for the case of incompressible fluid with constant density.

In this paper we use duality theory to associate certain measures to fully-nonlinear elliptic equations. These measures are the natural extension of the Mather measures to controlled stochastic processes and associated second-order elliptic equations. We apply these ideas to prove new a priori estimates for smooth solutions of fully nonlinear elliptic equations.