IJPAM: Volume 22, No. 2 (2005)

INSTABILITY OF PERIODIC WAVES OF
A VAN DER WAALS FLUID MODEL

Rita Cavazzonivia Firenze 4, 42100, Reggio Emilia, ITALY
Dipartimento di Matematica
Universitá Degli Studi di Firenze
S. Marco, 4 - 50121, Firenze, ITALY
e-mail: cavazzon@interfree.it


Abstract.We study a van der Waals fluid model and prove the existence of spatially-periodic travelling waves if and only if the velocity is zero. We prove the spectral instability of a stationary periodic wave: the spectral analysis is carried out by means of Floquet's theory. After introducing the Evans function $D(\lambda,\theta)$, the result about stability is achieved by means of a description of the zero set of $D$ around the origin. This zero set is described at the leading order by a formula which involves a flux of a suitable first-order system of conservation laws derived by means of homogenisation procedure.

Received: May 26, 2005

AMS Subject Classification: 35G20, 35P05

Key Words and Phrases: periodic waves, spectral stability, Evans function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 2