Homogenization of first order hyperbolic equations and application to miscible flow in porous media
type: Item
instance of: scholarly article
title: Homogenization of first order hyperbolic equations and application to miscible flow in porous media
zbMATH Open document ID: 0699.35170
DOI: 10.1016/S0294-1449(16)30317-1
author: Youcef Amirat
author: Kamel Hamdache
author: Abdelhamid Ziani
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78185
review text: The homogenization of the hyperbolic equation \[ \partial_ tu^{\varepsilon}+a^{\varepsilon}(t,y)\partial_ xu^{\varepsilon}=0,\quad t>0,\quad x\in {\mathbb R},\quad y\in \Omega \subset {\mathbb R}^ N \tag{1} \] with initial data and boundary conditions when \(x\in]0,1[\) is considered. For this purpose the \(L^{\infty}\)-weak*-limit of some holomorphic functions of the type \(\phi^{\varepsilon}_ y(\lambda)=(\lambda - A^{\varepsilon}(y))^{-1}\), \(\lambda\in {\mathbb C}\setminus [m,M]\) with \(0\leq m\leq A^{\varepsilon}(y)\leq M\) for a.e. \(y\), by using the integral representation of Nevanlinna-Pick's holomorphic functions is studied first.
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 4146642
zbMATH Keywords: hyperbolic equation
zbMATH Keywords: integral representation
zbMATH Keywords: Nevanlinna-Pick's holomorphic functions
MaRDI profile type: Publication
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OpenAlex ID: W2529594109
description: scientific article; zbMATH DE number 4146642