Search results for "equation"

Boundary value steady solutions of a class of hydrodynamic models for vehicular traffic flow

2003

This paper deals with the solution of a boundary value problem related to a steady nonuniform description of a class of traffic flow models. The models are obtained by the closure of the mass conservation equation with a phenomenological relation linking the local mass velocity to the local density. The analysis is addressed to define the proper framework toward the identification of the parameter characterizing the model. The last part of the paper develops a critical analysis also addressed to the design of new traffic flow models.

Solution of a cauchy problem for an infinite chain of linear differential equations

2005

Defining the recurrence relations for orthogonal polynomials we have found an exact solution of a Cauchy problem for an infinite chain of linear differential equations with constant coefficients. These solutions have been found both for homogeneous and an inhomogeneous systems.

The cauchy problem for non-linear Klein-Gordon equations

1993

We consider in ℝ n+1,n≧2, the non-linear Klein-Gordon equation. We prove for such an equation that there is a neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the …

Systèmes hyperboliques d'équations aux dérivées partielles linéaires : régularité et matrices diagonalisables

2001

Resume La regularite des solutions d'un systeme d'equations aux derivees partielles hyperbolique, est liee aux proprietes spectrales d'un faisceaux de matrices reelles. Nous nous interessons ici a la regularite L 2 . Celle ci est obtenue si et seulement si l'exponentielle imaginaire du faisceau est bornee. Nous regardons le lien entre cette condition et les proprietes spectrales du faisceau, ici diagonalisable sur R . Nous donnons en particulier un critere d'exponentielle bornee si les valeurs propres ne sont pas de multiplicites constantes, et nous montrons que dans le cas des faisceaux engendres par deux matrices 3×3, l'exponentielle est bornee si et seulement si le faisceau est analytiqu…

Exact treatment of linear difference equations with noncommutative coefficients

2007

The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.

Exact treatment of operator difference equations with nonconstant and noncommutative coefficients

2013

We study a homogeneous linear second-order difference equation with nonconstant and noncommuting operator coefficients in a vector space. We build its exact resolutive formula consisting of the explicit noniterative expression of a generic term of the unknown sequence of vectors. Some nontrivial applications are reported in order to show the usefulness and the broad applicability of the result.

Fully reliable a posteriori error control for evolutionary problems

2015

A nonhomogeneous nonlocal elasticity model

2006

Nonlocal elasticity with nonhomogeneous elastic moduli and internal length is addressed within a thermodynamic framework suitable to cope with continuum nonlocality. The Clausius–Duhem inequality, enriched by the energy residual, is used to derive the state equations and all other thermodynamic restrictions upon the constitutive equations. A phenomenological nonhomogeneous nonlocal (strain difference-dependent) elasticity model is proposed, in which the stress is the sum of two contributions, local and nonlocal, respectively governed by the standard elastic moduli tensor and the (symmetric positive-definite) nonlocal stiffness tensor. The inhomogeneities of the elastic moduli and of the int…

Quasilinear degenerate parabolic equations in unbounded domains

2004

We prove the existence of bounded solutions of Cauchy-Dirichlet problem associated to a degenerate parabolic equation of second order in divergence form in unbounded domain.

Theoretical study on travelling web dynamics and instability under non-homogeneous tension

2013

Problems of dynamics and stability of a moving web, travelling between two rollers at a constant velocity, are studied using analytical approaches. Transverse vibrations of the web are described by a partial differential equation that includes the centrifugal force, in-plane tension, elastic reaction and nonstationary inertial terms. The model of a thin elastic plate subjected to bending and non-homogeneous tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of studies of small out-of-plane vibrations. The influence of linearly distributed in-plane tension on the characteristics of the web vibration…