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Article type: Research Article
Authors: Petrini, Milena
Affiliations: Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy. E-mail: m.petrini@univpm.it
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
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