×

Uniform boundary stabilization of semilinear wave equation with nonlinear boundary damping. (English) Zbl 0819.35098

Joshi, Mohan C. (ed.) et al., Mathematical theory of control. Proceedings of the international conference, held at the Indian Institute of Technology, Bombay, India, Dec. 10-15, 1990. New York: Marcel Dekker, Inc. Lect. Notes Pure Appl. Math. 142, 233-254 (1993).
Summary: We consider semilinear wave equation with nonlinear boundary conditions. We assume that the energy dissipation occurs on a portion of the boundary via a nonlinear (noncoercive) velocity feedback. Under some technical conditions imposed on the nonlinear terms, we prove that the energy of the entire system decays uniformly to zero when the time \(t\to\infty\). In contrast with other works on related topics we do not assume any geometric coefficients on the controlled portion of the boundary.
For the entire collection see [Zbl 0771.00032].

MSC:

35L70 Second-order nonlinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
PDFBibTeX XMLCite