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,
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