Showing papers in "Annali Dell'universita' Di Ferrara in 2002"

Free Boundary Problem for the Equation of One-Dimensional Motion of Compressible Gas with Density-Dependent Viscosity.

Abstract: We consider a free boundary problem for the equation of the one-dimensional isentropic motion with density-dependent viscosity μ =b ϱ β, whereb and β are positive constants. We prove that there exists an unique weak solution globally in time, provided that β<1/3.

Gelfand spaces and pseudodifferential operators of infinite order in ℝn

Abstract: The aim of this work is to study a class of symbols of infinite order and to develop a global calculus for the corresponding pseudodifferential operators. In particular, we obtain results of boundedness for the operators and of global regularity for the solutions of the associated equations in the Gelfand spaces.

The stability of constant equilibrium states in relaxation models

Abstract: We consider various first-order systems of PDEs with partial dissipation, as well as partial conservation. This class includes relaxation models, for instance the one designed by S. Jin and Z. Xin, as well as discrete velocity models for gases, as the Broadwell system. As we showed in a recent paper, the Jin-Xin model admits a convex compact positively invariant region, whenever the equilibrium system does. As a by-product, we obtained the existence of global weak solutions for the Cauchy problem with large data. For more general systems, the global existence of a uniformly bounded entropy solution will be a basic assumption in this work. We consider one-dimensional data which are either space periodic or square integrable. We prove that the (expected globally bounded) entropy solution relaxes to the equilibrium state; the latter is either zero or is determined by the mean value of the conserved components. We emphasize that we do not need any assumption about the nonlinearity of the underlying equilibrium system. We give two different proofs of the stabilization, which apply in different contexts. The first one uses compensated compactness and has a rather broad efficiency. For instance, it applies to several quasi-linear models. But the convergence result does not provide any decay rate in the periodic setting. The other one uses a dispersion estimate for the principal part of the model. It applies to periodic data and needs the strong assumption of semi-linearity, but yields an exponential decay in theL2-norm. We expect that it could extend to multi-dimensional contexts.

Asymptotic behaviour for electromagnetic fields in the ionosphere

Abstract: We consider the linear theory of the Electromagnetism in the ionosphere characterized by a constitutive equation which associates the presence of memory effects with the actual action of the electric field. After studying the thermodynamic restrictions on the assumed constitutive equations, a domain of dependence inequality is derived. Then, asymptotic behaviour of solutions is studied together with uniqueness and existence theorems.

Projective version of Malcolmson’s criterion

Abstract: It is proven that the extension of Malcolmson’s methods to reppresent all elements ofRζ is not purely straightforward. A detailed proof of such extension is here furnished.

A curious behavior of capillary surfaces

Abstract: It is known that for a given base domainΩ and «contact angle»γ, there will be a critical γ0, 0 ⩽γ0, ⩽π/2., such that a solution overΩ of the scalar capillarity equation in the absence of external (e.g. gravity) force field will exist if γ0, 0 ⩽γ, ⩽π/2, and will fail to exist if 0 ⩽γ ⩽γ0. In the particular case for whichΩ is a circular disk, a solution exists for everyγ, and is unique up to an additive constant. For a piecewise smoothΩ that is not circular, there will be a boundary pointP of maximal inward directed curvatureKM (at a protruding corner we defineKM=∞). We suppose that a solution exists for such a domain, and ask whether a solution continues to exist if the domain is made closer to circular by smoothing with an inscribed interior arc of constant curvatureK

Absolute Gradient Bounds for Nonparametric Hypersurfaces of Constant Mean Curvature.

Abstract: We consider the problem of determining the existence of absolute apriori gradient bounds of nonparametric hypersurfaces of constant mean curvature in ann-dimensional sphereBR, 1>R>R0(n), (R0(n) being a constant depending only onn), without imposing boundary conditions or bounds of any sort.

A feasible-direction method for nonlinear constrained optimization

Abstract: In this paper we describe and analyse a numerical method presented by Herskovits for the solution of the nonlinear programming problem with inequality constraints. We propose some new updating rules for the parameters of the algorithm and show that these rules are valid and efficient.

Mathematical study of the small oscillations of an incompressible and inviscid liquid under zero gravity in a container of revolution with elastic bottom and anchored edge

Abstract: In this paper, the Authors study the small oscillations of an inviscid liquid under zero gravity in a container of revolution with elastic bottom, considered as a membrane or a plate, and anchored edge. They obtain the equations of the displacements of the free surface and the bottom and they reduce these equations to a functional equation in a suitable Hilbert space. By using the methods of Functional Analysis the Authors prove the existence of the small oscillations.

On a quadratic functional occurring in a bivariate scattered data interpolation problem

Abstract: L’applicazione di noti metodi che utilizzano funzioni di tipo blending per la costruzione di funzioni bivariate C1 per l’interpolazione di dati, richiede la conoscenza delle derivate parziali del primo ordine ai vertici di una triangolazione sottostante. In questo lavoro consideriamo il metodo proposto da Nielson, che consiste nel calcolare stime delle derivate parziali del primo ordine minimizzando un opportuno funzionale quadratico, caratterizzato da parametri di tensione non negativi. Scopo del lavoro e l’analisi di alcune proprieta particolari di questo funzionale per la costruzione di algoritmi efficienti e robusti per la determinazione delle stime suddette delle derivate quando si ha a che fare con insiemi di dati di grandi dimensioni. Abstract The application of widely known blending methods for constructingC 1 bivariate functions interpolating scattered data requires the knowledge of the partial derivatives of first order at the vertices of an underlying triangulation. In this paper we consider the method proposed by Nielson that consists in computing estimates of the first order partial derivatives by minimizing an appropriate quadratic functional, characterized by nonnegative tension parameters. The aim of the paper is to analyse some peculiar properties of this functional in order to construct robust and efficient algorithms for determining the above estimates of the derivatives when we are concerned with extremely large data sets.

Holomorphic vector bundles on compact complex non-algebraic surfaces

Abstract: LetX be a smooth complex compact surface without non-constant meromorphic functions. Here we prove the existence of rank holomorphic vector bundles onX containing exactly one rank one saturated subsheaf.

Spatial energy decay estimate in dynamical problems for a micropolar viscoelastic solid

Abstract: We consider a linear micropolar viscoelastic solid occupying a domainB in dynamical conditions. First, on assuming thatB is of the kindB={∈R:x’ =(x1,x2)∈D(x3);x3∈R++}, and that the body is subjected to boundary data different from zero only onD(0), we estimate for any fixedt>0, in terms of the initial and boundary data, the «energy» of the portions of the solid at distance greater thanz fromD(0)(gt(z)) and its norm inL1(0,t) (Gt(z)). Moreover we show that, if there exists somez0≥0, such that past histories vanish onD(z) withz≥z0, then for any fixedt>0 the points (x’’, z) withz−z0≥Vt are at rest, while forz−z0≤Vt, Gt(z) decays withz−z0, the decay rate being described by the factor \(1 - \frac{{z - z_0 }}{{Vt}}\).V is a computable positive constant depending on the relaxation functions, the mass density and the microinertial tensor. Finally these last results are extended to more general domains under the hypothesis that the initial and boundary data have a bounded support. In our analysis we make use of a Maximal Free Energy which allows us to impose very mild restrictions on the relaxation functions.

Dinamica relativa di una particella con spin: un teorema di unicità

Abstract: We prove anunicity theorem for spinning particles in the Papapetrou-Tulczyjew scheme; the theorem modifies the conclusive remarks of a preceding paper [1], ie the erroneous incompatibility of such scheme The unicity is given using an intrinsic frame of reference (parallel to the generalized impulsion) and theresolvent equation of the differential problem, in terms of velocity (vectorial parameter)

Periodic solutions for the transport of a pollutant concentration in a porous medium

Abstract: We study the existence and uniqueness of the periodic solution for a model which describes the transport of a pollutant in a porous medium, with periodic boundary conditions. The prove of existence, is based upon a topological tool as the Schauder fixed point theorem, applied to a PDE. The uniqueness is instead of obtained, assuming thats→d i,j(x,ϕ –1(s)) is Holder continuous of order γ∈ ∈ (1/2, 1).

Riferimenti isotropi in relatività generale

Abstract: We consider anew approach for a relativistic frame of reference in the polar sense [1] (two-congruences) and the related non-holonomic techniques for anull congruence (light flux); 1° order characteristic tensors, Ricci rotation coefficients, longitudinal and transversal covariant derivatives are deduced in general form Thus, the method of a standard frame of reference is extended to thenull case