Issue |
ESAIM: COCV
Volume 12, Number 2, April 2006
|
|
---|---|---|
Page(s) | 231 - 252 | |
DOI | https://doi.org/10.1051/cocv:2006001 | |
Published online | 22 March 2006 |
Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping
Department of Mathematics,
Washington State University, Pullman, WA 99164-3113,
USA;
khapala@math.wsu.edu
Received:
31
March
2004
Revised:
9
December
2004
We show that the set of nonnegative equilibrium-like states, namely, like of the semilinear vibrating string that can be reached from any non-zero initial state
, by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace
of
. Our main results deal with nonlinear terms which admit at most the linear
growth at infinity in
and satisfy certain restriction on their total impact on (0,∞) with respect to the time-variable.
Mathematics Subject Classification: 93 / 35
Key words: Semilinear wave equation / approximate controllability / multiplicative controls / axial load / damping.
© EDP Sciences, SMAI, 2006
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