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Homogenization of a spectral equation with drift in linear transport

Guillaume Bal (2001)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with the homogenization of a spectral equation posed in a periodic domain in linear transport theory. The particle density at equilibrium is given by the unique normalized positive eigenvector of this spectral equation. The corresponding eigenvalue indicates the amount of particle creation necessary to reach this equilibrium. When the physical parameters satisfy some symmetry conditions, it is known that the eigenvectors of this equation can be approximated by the product of two...

Homogenization of a spectral equation with drift in linear transport

Guillaume Bal (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with the homogenization of a spectral equation posed in a periodic domain in linear transport theory. The particle density at equilibrium is given by the unique normalized positive eigenvector of this spectral equation. The corresponding eigenvalue indicates the amount of particle creation necessary to reach this equilibrium. When the physical parameters satisfy some symmetry conditions, it is known that the eigenvectors of this equation can be approximated by the product...

Homogenization of monotone systems of Hamilton-Jacobi equations

Fabio Camilli, Olivier Ley, Paola Loreti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the uniform convergence of the solution of the oscillating systems to the bounded uniformly continuous solution of the homogenized system.

How many are affine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2014)

Archivum Mathematicum

The question how many real analytic affine connections exist locally on a smooth manifold M of dimension n is studied. The families of general affine connections with torsion and with skew-symmetric Ricci tensor, or symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of n variables.

How many are equiaffine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2015)

Archivum Mathematicum

The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold M of dimension n is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of n variables.

Implicit difference methods for nonlinear first order partial functional differential systems

Elżbieta Puźniakowska-Gałuch (2010)

Applicationes Mathematicae

Initial problems for nonlinear hyperbolic functional differential systems are considered. Classical solutions are approximated by solutions of suitable quasilinear systems of difference functional equations. The numerical methods used are difference schemes which are implicit with respect to the time variable. Theorems on convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability is based on a comparison technique with nonlinear estimates...

Lagrangian approach to deriving energy-preserving numerical schemes for the Euler–Lagrange partial differential equations

Takaharu Yaguchi (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose a Lagrangian approach to deriving energy-preserving finite difference schemes for the Euler–Lagrange partial differential equations. Noether’s theorem states that the symmetry of time translation of Lagrangians yields the energy conservation law. We introduce a unique viewpoint on this theorem: “the symmetry of time translation of Lagrangians derives the Euler–Lagrange equation and the energy conservation law, simultaneously.” The proposed method is a combination of a discrete counter...

Layering methods for nonlinear partial differential equations of first order

Avron Douglis (1972)

Annales de l'institut Fourier

This paper is concerned with generalized, discontinuous solutions of initial value problems for nonlinear first order partial differential equations. “Layering” is a method of approximating an arbitrary generalized solution by dividing its domain, say a half-space t ≥ 0 , into thin layers ( i - ℓ ) h ≤ t ≤ i h , i = 1 , 2 , ... ( h > 0 ) , and using a strict solution u i in the i -th layer. On the interface t = ( i - ℓ ) h , u t is required to reduce to a smooth function approximating the values on that plane of u i - ℓ . The resulting stratified configuration of strict solutions...

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