ASYMPTOTICS FOR THE SOLUTIONS OF ELLIPTIC SYSTEMS WITH RAPIDLY OSCILLATING COEFFICIENTS

0338784 - ÚJF 2010 RIV US eng J - Journal Article
Borisov, Denis I.
ASYMPTOTICS FOR THE SOLUTIONS OF ELLIPTIC SYSTEMS WITH RAPIDLY OSCILLATING COEFFICIENTS.
St Petersburg Mathematical Journal. Roč. 20, č. 2 (2009), s. 175-191. ISSN 1061-0022. E-ISSN 1547-7371
R&D Projects: GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : Homogenization of differentiable operators * unbounded domain * fast and slow variables
Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders

A singularly perturbed second order elliptic system in the entire space is treated. The coefficients of the systems oscillate rapidly and depend on both slow and fast variables. The homogenized operator is obtained and, in the uniform norm sense, the leading terms of the asymptotic expansion are constructed for the resolvent of the operator described by the system. The convergence of the spectrum is established, and examples are given.
Permanent Link: http://hdl.handle.net/11104/0182466