Article ID Journal Published Year Pages File Type
1707395 Applied Mathematics Letters 2016 7 Pages PDF
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, ∂t2un−∂x2un=∂tf and un−∂x2un=f on the respective spatial domains ⋃j∈{1,…,n}(j−1n,2j−12n) and ⋃j∈{1,…,n}(2j−12n,jn). We show that (un)n(un)n converges weakly to uu, which solves the exponentially stable limit equation ∂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.

Related Topics
Physical Sciences and Engineering Engineering Computational Mechanics
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