Stabilization via Homogenization

Marcus Waurick

Research output: Contribution to journalArticle

8 Citations (Scopus)
218 Downloads (Pure)

Abstract

In this short note we treat a 1+11+1-dimensional system of changing type. On different spatial domains the system is of hyperbolic and elliptic type, that is, formally, View the MathML source∂t2un−∂x2un=∂tf and View the MathML sourceun−∂x2un=f on the respective spatial domains View the MathML source⋃j∈{1,…,n}(j−1n,2j−12n) and View the MathML source⋃j∈{1,…,n}(2j−12n,jn). We show that (un)n(un)n converges weakly to uu, which solves the exponentially stable limit equation View the MathML source∂t2u+2∂tu+u−4∂x2u=2(f+∂tf) on [0,1][0,1]. If the elliptic equation is replaced by a parabolic one, the limit equation is not exponentially stable.
Original languageEnglish
Pages (from-to)101-107
JournalApplied Mathematics Letters
Volume60
Early online date28 Apr 2016
DOIs
Publication statusPublished - Oct 2016

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