Spectral analysis and transport of energy density for an hyperbolic system with periodic oscillations

Article type: Research Article

Authors: Petrini, Milena

Affiliations: Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy. E-mail: [email protected]

Abstract: We deal with an hyperbolic degenerate system with periodic oscillations in the lower order term and principal part with characteristics of variable multiplicity. In the homogenization limit the effective system does not present a memory term, however it loses the property of energy conservation. A spectral analysis on the Bloch space is worked out for the system in some particular case of oscillating term. Through a decomposition in Bloch waves we determine the transport for the limiting energy density related to the solution a Cauchy problem with oscillatory initial data.

Keywords: homogenization, spectral theory and eigenvalues problems for partial differential operators, Wigner measures

DOI: 10.3233/ASY-2012-1125

Journal: Asymptotic Analysis, vol. 81, no. 2, pp. 135-156, 2013