This note deals with a doubly-nonlinear parabolic-hyperbolic equation, that represents electromagnetic processes in a nonhomogeneous metal surrounded by an insulating environment. Existence of a weak solution is here illustrated. The constitutive relations are then assumed to exhibit periodic oscillations in space. As the period vanishes, the solution converges in the sense of Nguetseng to that of a corresponding two-scale homogenized problem. The homogenization procedure is then completed by eliminating the dependence on the fine-scale variable. An analogous problem issued from phase transitions is also illustrated.
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Augusto Visintin, Homogenization of doubly-nonlinear equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 3, pp. 211–222DOI 10.4171/RLM/464