All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 19 Next

Displaying 361 – 380 of 681

Showing per page

A variational approach to implicit ODEs and differential inclusions

Sergio Amat, Pablo Pedregal (2009)

ESAIM: Control, Optimisation and Calculus of Variations

An alternative approach for the analysis and the numerical approximation of ODEs, using a variational framework, is presented. It is based on the natural and elementary idea of minimizing the residual of the differential equation measured in a usual Lp norm. Typical existence results for Cauchy problems can thus be recovered, and finer sets of assumptions for existence are made explicit. We treat, in particular, the cases of an explicit ODE and a differential inclusion. This approach also allows...

A variational inequality for discontinuous solutions of degenerate parabolic equations.

Lorina Dascal, Shoshana Kamin, Nir A. Sochen (2005)

RACSAM

The Beltrami framework for image processing and analysis introduces a non-linear parabolic problem, called in this context the Beltrami flow. We study in the framework for functions of bounded variation, the well-posedness of the Beltrami flow in the one-dimensional case. We prove existence and uniqueness of the weak solution using lower semi-continuity results for convex functions of measures. The solution is defined via a variational inequality, following Temam?s technique for the evolution problem...

A variational model for equilibrium problems in a traffic network

Giandomenico Mastroeni, Massimo Pappalardo (2004)

RAIRO - Operations Research - Recherche Opérationnelle

We propose a variational model for one of the most important problems in traffic networks, namely, the network equilibrium flow that is, traditionally in the context of operations research, characterized by minimum cost flow. This model has the peculiarity of being formulated by means of a suitable variational inequality (VI) and its solution is called “equilibrium”. This model becomes a minimum cost model when the cost function is separable or, more general, when the jacobian of the cost operator...

A variational model for equilibrium problems in a traffic network

Giandomenico Mastroeni, Massimo Pappalardo (2010)

RAIRO - Operations Research

We propose a variational model for one of the most important problems in traffic networks, namely, the network equilibrium flow that is, traditionally in the context of operations research, characterized by minimum cost flow. This model has the peculiarity of being formulated by means of a suitable variational inequality (VI) and its solution is called “equilibrium”. This model becomes a minimum cost model when the cost function is separable or, more general, when the Jacobian of the cost operator...

A variational model for urban planning with traffic congestion

Guillaume Carlier, Filippo Santambrogio (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.

A variational model for urban planning with traffic congestion

Guillaume Carlier, Filippo Santambrogio (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.

A variational model in image processing with focal points

Andrea Braides, Giuseppe Riey (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a model for segmentation problems involving an energy concentrated on the vertices of an unknown polyhedral set, where the contours of the images to be recovered have preferred directions and focal points. We prove that such an energy is obtained as a Γ-limit of functionals defined on sets with smooth boundary that involve curvature terms of the boundary. The minimizers of the limit functional are polygons with edges either parallel to some prescribed directions or pointing to some fixed...

A variational problem for couples of functions and multifunctions with interaction between leaves

Emilio Acerbi, Gianluca Crippa, Domenico Mucci (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We discuss a variational problem defined on couples of functions that are constrained to take values into the 2-dimensional unit sphere. The energy functional contains, besides standard Dirichlet energies, a non-local interaction term that depends on the distance between the gradients of the two functions. Different gradients are preferred or penalized in this model, in dependence of the sign of the interaction term. In this paper we study the lower semicontinuity and the coercivity of the energy...

A variational problem modelling behavior of unorthodox silicon crystals

J. Hannon, M. Marcus, Victor J. Mizel (2003)

ESAIM: Control, Optimisation and Calculus of Variations

Controlling growth at crystalline surfaces requires a detailed and quantitative understanding of the thermodynamic and kinetic parameters governing mass transport. Many of these parameters can be determined by analyzing the isothermal wandering of steps at a vicinal [“step-terrace”] type surface [for a recent review see [4]]. In the case of o r t h o d o x crystals one finds that these meanderings develop larger amplitudes as the equilibrium temperature is raised (as is consistent with the statistical mechanical...

A Variational Problem Modelling Behavior of Unorthodox Silicon Crystals

J. Hannon, M. Marcus, Victor J. Mizel (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Controlling growth at crystalline surfaces requires a detailed and quantitative understanding of the thermodynamic and kinetic parameters governing mass transport. Many of these parameters can be determined by analyzing the isothermal wandering of steps at a vicinal [“step-terrace”] type surface [for a recent review see [4]]. In the case of orthodox crystals one finds that these meanderings develop larger amplitudes as the equilibrium temperature is raised (as is consistent with the statistical...

A variational solution of the A. D. Aleksandrov problem of existence of a convex polytope with prescribed Gauss curvature

Vladimir Oliker (2005)

Banach Center Publications

In his book on convex polytopes [2] A. D. Aleksandrov raised a general question of finding variational formulations and solutions to geometric problems of existence of convex polytopes in ℝ n + 1 , n ≥ 2, with prescribed geometric data. Examples of such problems for closed convex polytopes for which variational solutions are known are the celebrated Minkowski problem [2] and the Gauss curvature problem [20]. In this paper we give a simple variational proof of existence for the A. D. Aleksandrov problem...

A variationally consistent generalized variable formulation of the elastoplastic rate problem

Claudia Comi, Umberto Perego (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The elastoplastic rate problem is formulated as an unconstrained saddle point problem which, in turn, is obtained by the Lagrange multiplier method from a kinematic minimum principle. The finite element discretization and the enforcement of the min-max conditions for the Lagrangean function lead to a set of algebraic governing relations (equilibrium, compatibility and constitutive law). It is shown how important properties of the continuum problem (like, e.g., symmetry, convexity, normality) carry...

Currently displaying 361 – 380 of 681