Homogenization of linear and nonlinear ordinary differential equations with time depending coefficients
type: Item
instance of: scholarly article
title: Homogenization of linear and nonlinear ordinary differential equations with time depending coefficients
zbMATH Open document ID: 0907.34045
author: Milena Petrini
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1999-03-02T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108469
review text: Summary: The author studies the effective behaviour of solutions to the linear equation \(\partial_tu^\varepsilon+ a^\varepsilon(t, x)u^\varepsilon= 0\) and to the nonlinear nonhomogeneous Riccati equation \(\partial_tu^\varepsilon+ a^\varepsilon(t, x)(u^\varepsilon)^2= f(t, x)\), \(f>0\), when \(a^\varepsilon\rightharpoonup a\) in \(L^\infty\) weak\(^*\) and data at time \(t= 0\) are nonoscillating. In the first case, the limit is an integro-differential equation and the memory term is described by a resolvent Volterra equation. Existence and uniqueness for the solution to the effective equations are proved by passing to a kinetic formulation. On the other side the Riccati equation reveals the phenomenon of instantaneous memory, described through an asymptotic approach that consists in looking for an expansion by introducing a suitable parameter.
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1183136
zbMATH Keywords: Riccati equation
zbMATH Keywords: integro-differential equation
zbMATH Keywords: Volterra equation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1183136