Homogenisation theory for Friedrichs systems. (English) Zbl 1284.35045
Summary: We develop a general homogenisation procedure for Friedrichs systems. Under reasonable assumptions, the concepts of \(G\) and \(H\)-convergence are introduced. As Friedrichs systems can be used to represent various boundary or initial-boundary value problems for partial differential equations, some additional assumptions are needed for compactness results. These assumptions are particularly examined for the stationary diffusion equation, the heat equation and a model example of a first order equation leading to memory effects. In the first two cases, the equivalence with the original notion of \(H\)-convergence is proved.
MSC:
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 35F45 | Boundary value problems for systems of linear first-order PDEs |
| 35M32 | Boundary value problems for mixed-type systems of PDEs |
| 47F05 | General theory of partial differential operators |
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