Catálogo de publicaciones - libros

In this paper, in the framework of a problem related to an elastic non homogeneous medium, we deal with a periodic coupled force $$ (f(x)/\varepsilon ^\alpha ) \vec F (x/\varepsilon ) $$ with intensity of order 1/ ε ^α. The parameter ε is connected with the period of the non homogeneity of the medium and with the periodicity of the coupled force. The determination of the parameter α is the target of our study to obtain an effect in the microscopic equation. The homogenization technique is used in order to study the equation: $$ - (\partial /\partial x_j ) (a_{ijkh} (x/\varepsilon ) e_{kh} (\vec u^{\varepsilon ,\alpha } )) = (f(x)/\varepsilon ^\alpha ) F_i (x/\varepsilon ) + G_i (x,x/\varepsilon ) $$ , where G _ i (x,x/ε) is the volume applied force. The limit, when ε → 0, of $$ \vec u^{\varepsilon ,\alpha } (x) $$ , in the sense of two scale convergence, is $$ (\vec u^{0,\alpha } (x), \vec u^{1,\alpha } (x,y)) $$ and the microscopic equation becomes: $$ - (\partial /\partial y_j ) (a_{ijkh} (y) e_{khx} (\vec u^{0,\alpha } (x))) - (\partial /\partial y_j ) (e_{khy} (\vec u^{1,\alpha } (x,y))) = f(x) F_i (y) $$ if $$ \alpha = 1, - (\partial /\partial y_j ) (a_{ijkh} (y) e_{khx} (\vec u^{0,\alpha } (x)) + e_{khy} (\vec u^{1,\alpha } (x,y))) = 0 $$ if 0 > α > 1. When α < 1 the solutions are not uniformly bounded respect to ε.

We continue our study on the approximation of a system of partial differential equations recently proposed by Hadeler and Kuttler to model the dynamics of growing sandpiles on a flat bounded table. The novelty here is the introduction of (infinite) walls on the boundary of the domain and the corresponding modification of boundary conditions for the standing and for the rolling layers. An explicit finite difference scheme is introduced and new boundary conditions are analyzed. We show experiments in ID and 2D which characterize the steady-state solutions.

We study the problem of urban areas detection from satellite images. In particular, we consider two types of satellite images: SAR (Synthetic Aperture Radar) images and optical images. We describe a simple algorithm for the detection of urban areas. We show that the performance of the detection algorithm can be improved using a fusion procedure of the SAR and optical images considered. The fusion algorithm presented in this paper is based on a simple use of ideas taken from calculus of variations and it makes possible to do together the filtering and the data fusion steps. Some numerical examples obtained processing real data are reported at the end of the paper. In the website http: //web. unicam. it/ matinf /f atone/wl several animations relative to these numerical examples can be seen.

In this work we discuss the development of fast algorithms for the inelastic Boltzmann equation describing the collisional motion of a granular gas. In such systems the collisions between particles occur in an inelastic way and are characterized by a coefficient of restitution which in the general case depends on the relative velocity of the collision. In the quasi-elastic approximation the granular operator is replaced by the sum of an elastic Boltzmann operator and a nonlinear friction term. Fast numerical methods based on a suitable spectral representation of the approximated model are then presented.

In this paper we study controllability properties of linear degenerate parabolic equations. Due to degeneracy, classical null controllability results do not hold in general. Thus we investigate results of’ regional null controllability’, showing that we can drive the solution to rest at time T on a subset of the space domain, contained in the set where the equation is nondegenerate.

The mass balance equation for stationary flow in a confined aquifer and the phenomenological Darcy’s law lead to a classical elliptic PDE, whose phenomenological coefficient is transmissivity, T , whereas the unknown function is the piezometric head. The differential system method (DSM) allows the computation of T when two “independent” data sets are available, i.e., a couple of piezometric heads and the related source or sink terms corresponding to different flow situations such that the hydraulic gradients are not parallel at any point. The value of T at only one point of the domain, x_0, is required. The T field is obtained at any point by integrating a first order partial differential system in normal form along an arbitrary path starting from x_0. In this presentation the advantages of this method with respect to the classical integration along characteristic lines are discussed and the DSM is modified in order to cope with multiple sets of data. Numerical tests show that the proposed procedure is effective and reduces some drawbacks for the application of the DSM.

A quadratic cheap control of linear systems with multiple state delays is considered. This optimal control problem is transformed to an optimal control problem of singularly perturbed systems. A composite suboptimal control of the latter is designed based on its asymptotic decomposition into two much simpler parameter-free subproblems, the slow and fast ones. Using this composite control, a suboptimal control of the original cheap control problem is constructed and justified for two classes of the initial function for the state variable. An illustrative example is presented.

Perturbations of Karush-Kuhn-Tucker conditions play an important role for primal-dual interior point methods. Beside the usual logarithmic barrier various further techniques of sequential unconstrained minimization are well known. However other than logarithmic embeddings are rarely studied in connection with Newton path-following methods. A key property that allows to extend the class of methods is the existence of a locally Lipschitz continuous path leading to a primal-dual solution of the KKT-system. In this paper a rather general class of barrier/penalty functions is studied. In particular, under LICQ regularity and strict complementarity assumptions the differentiability of the path generated by any choice of barrier/penalty functions from this class is shown. This way equality as well as inequality constraints can be treated directly without additional transformations. Further, it will be sketched how local convergence of the related Newton path-following methods can be proved without direct applications of self-concordance properties.

The paper investigates stationarity and regularity concepts for set systems in a normed space. Several primal and dual constants characterizing these properties are introduced and the relations between the constants are established. The equivalence between the regularity property and the strong metric inequality is established. The extended extremal principle is formulated.

We consider the problem of modeling dynamic thin shells with thermal effects based on the intrinsic geometry methods of Michel Delfour and Jean-Paul Zolésio. This model relies on the oriented distance function which describes the geometry. Here we further develop the Kirchhoff-based shell model introduced in our previous work by subjecting the elastically and thermally isotropic shell to an unknown temperature distribution. This yields a fully-coupled system of four linear equations whose variables are the displacement of the shell mid-surface and the thermal stress resultants.