On the theory of homogenization of evolutionary equations in Hilbert spaces

Details On the theory of homogenization of evolutionary equations in Hilbert spaces On the theory of homogenization of evolutionary equations in Hilbert spaces

2012-04-17

arxiv.org/abs/1204.3768v1

Mathematics

Analysis of PDEs

34 pages

Scientific paper

We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics. In particular, we give a unified treatment for (non-)periodic homogenization problems in thermodynamics, elasticity, electro-magnetism and coupled systems. The approach also permits the consideration of memory problems in anisotropic media which, in the context of Maxwell's equations, may be summarized by the umbrella terms bi-anisotropic and dissipative. Moreover, we show that the limiting equation is well-posed and causal and we prove that the principal physical phenomenon remains unchanged after the homogenization process.

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