HOMOGENISATION THEORY FOR FRIEDRICHS SYSTEMS

作者：Burazin Kresimir^*; Vrdoljak Marko

来源：Communications on Pure and Applied Analysis, 2014, 13(3): 1017-1044.

DOI：10.3934/cpaa.2014.13.1017

• Homogenisation
• symmetric positive systems
• H-convergence
• G-convergence
• compensated compactness

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.

• 出版日期2014-5