Naslov
Graph representation for asymptotic expansion in homogenisation of nonlinear first-order equations

Autori
Antonić, Nenad ; Burazin, Krešimir

Izvornik
Annali dell'Università di Ferrara. Sezione 7: Scienze matematiche (0430-3202) 53 (2007), 2; 149-176

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Homogenisation; memory effects; nonlinear equations

Sažetak
Homogenisation of a linear transport equation leads to an integro-differential equation with the differential part of the same type as the starting equation. The (nonperiodic) homogenisation of semilinear transport equations is open. In order to pinpoint technical difficulties, as a first step in that direction, following the approach of Tartar we consider an ordinary differential equation with an oscillating coefficient $a$: $u' +au^2=f, u(0)=v$ instead, and expand the solution in terms of a small parameter (the size of oscillations in $a$). The crucial observation we made is a correspondence between multiple inte\-grals representing the terms in asymptotic expansion of the solution and certain graphs, which allows easy manipulation of otherwise highly complicated expressions, and leads to efficient computation of the terms in expansion.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA