Search results for "auch"

A logarithmic fourth-order parabolic equation and related logarithmic Sobolev inequalities

2006

A logarithmic fourth-order parabolic equation in one space dimension with periodic boundary conditions is studied. This equation arises in the context of fluctuations of a stationary nonequilibrium interface and in the modeling of quantum semiconductor devices. The existence of global-in-time non-negative weak solutions and some regularity results are shown. Furthermore, we prove that the solution converges exponentially fast to its mean value in the ``entropy norm'' and in the Fisher information, using a new optimal logarithmic Sobolev inequality for higher derivatives. In particular, the rate is independent of the solution and the constant depends only on the initial value of the entropy.

Explicit solutions for a system of coupled Lyapunov differential matrix equations

1987

This paper is concerned with the problem of obtaining explicit expressions of solutions of a system of coupled Lyapunov matrix differential equations of the typewhere Fi, Ai(t), Bi(t), Ci(t) and Dij(t) are m×m complex matrices (members of ℂm×m), for 1≦i, j≦N, and t in the interval [a,b]. When the coefficient matrices of (1.1) are timeinvariant, Dij are scalar multiples of the identity matrix of the type Dij=dijI, where dij are real positive numbers, for 1≦i, j≦N Ci, is the transposed matrix of Bi and Fi = 0, for 1≦i≦N, the Cauchy problem (1.1) arises in control theory of continuous-time jump linear quadratic systems [9–11]. Algorithms for solving the above particular case can be found in [1…

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.

Stellar hydrodynamics with glaister's riemann solver: An approach to the stellar collapse

1990

La resolution de Remann approximee de la solution des equations d'Euler de la dynamique des gaz 1 D, developpee par Glaister P. (1988, J. Comput. Phys., 74) est introduite dans un code hydrodynamique lagrangien et appliquee a l'effondrement stellaire a symetrie spherique

Regularity of solutions of cauchy problems with smooth cauchy data

1988

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…

Existence results and asymptotic behavior for nonlocal abstract Cauchy problems

2008

AbstractThe purpose of this paper is to study the existence and asymptotic behavior of solutions for Cauchy problems with nonlocal initial datum generated by accretive operators in Banach spaces.

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.