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Volume 14,     Number 3,     Fall 2006

 

ON THE DETERMINATION OF LIMITS FOR
SOME SEQUENCES OF FUNCTIONS AND
DIFFERENTIAL OPERATORS
A. HOLMBOM, M. OLSSON AND J. SILFVER

Abstract. The main concern of this paper is to study methods to determine the effective properties of various kinds of heterogeneous materials, and in particular to distinguish between which disturbances that can and cannot be neglected. In this connection we discuss limits for pairs of weakly convergent sequences, and the relation between such limits of traditional types and some different versions of two-scale convergence. These ideas are applied to characterize H-limits for some sequences of elliptic partial differential equations. Numerical experiments are performed to investigate the process when the determination of the limits becomes non-trivial.

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© 2006, Canadian Applied Mathematics Quarterly (CAMQ)