Differential and Integral Equations

Homogenization of ordinary and linear transport equations

Roberto Peirone

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Abstract

The homogenization of first order ordinary differential equations in $\mathbb{R}^N$ and associated linear transport equations are studied. We prove the equivalence between $G$-convergence and strong $G$-convergence for the ordinary equations. We give a sufficient condition, which is also necessary in the autonomous case, for the weak homogenization of the linear transport equations. This condition is satisfied when div$_x f=0$.

Article information

Source
Differential Integral Equations, Volume 9, Number 2 (1996), 323-334.

Dates
First available in Project Euclid: 3 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367603349

Mathematical Reviews number (MathSciNet)
MR1364051

Zentralblatt MATH identifier
0851.35014

Subjects
Primary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]
Secondary: 34A34: Nonlinear equations and systems, general 35F10: Initial value problems for linear first-order equations

Citation

Peirone, Roberto. Homogenization of ordinary and linear transport equations. Differential Integral Equations 9 (1996), no. 2, 323--334. https://projecteuclid.org/euclid.die/1367603349


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