Velocity Stabilization of a Wave Equation with a Nonlinear Dynamic Boundary Condition
Analysis of PDEs
2022-08-31 v1
Abstract
This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on the velocity at the controlled extremity. The uncontrolled boundary is subject to a nonlinear first-order term, which may represent nonlinear boundary anti-damping. Initial data is taken in the optimal energy space associated with the problem. Exponential decay of the mechanical energy is investigated in different cases. Stability and attractivity of suitable invariant sets are established.
Keywords
Cite
@article{arxiv.2208.14014,
title = {Velocity Stabilization of a Wave Equation with a Nonlinear Dynamic Boundary Condition},
author = {Nicolas Vanspranghe and Francesco Ferrante and Christophe Prieur},
journal= {arXiv preprint arXiv:2208.14014},
year = {2022}
}
Comments
IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, In press