Displaying similar documents to “Homogenization of the Maxwell Equations: Case II. Nonlinear conductivity”

Homogenization of the Maxwell equations: Case I. Linear theory

Niklas Wellander (2001)

Applications of Mathematics

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The Maxwell equations in a heterogeneous medium are studied. Nguetseng’s method of two-scale convergence is applied to homogenize and prove corrector results for the Maxwell equations with inhomogeneous initial conditions. Compactness results, of two-scale type, needed for the homogenization of the Maxwell equations are proved.

Homogenization of parabolic equations an alternative approach and some corrector-type results

Anders Holmbom (1997)

Applications of Mathematics

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We extend and complete some quite recent results by Nguetseng [Ngu1] and Allaire [All3] concerning two-scale convergence. In particular, a compactness result for a certain class of parameterdependent functions is proved and applied to perform an alternative homogenization procedure for linear parabolic equations with coefficients oscillating in both their space and time variables. For different speeds of oscillation in the time variable, this results in three cases. Further, we prove...

Propagation of electromagnetic waves in non-homogeneous media

Radjesvarane Alexandre, Hassan Taha (2004)

Applications of Mathematics

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We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations.