%0 Journal Article
%T Dissipative boundary conditions for nonlinear 1-D hyperbolic systems: sharp conditions through an approach via time-delay systems
%A Jean-Michel Coron
%A Hoai-Minh Nguyen
%J Mathematics
%D 2014
%I arXiv
%X We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a previous known sufficient condition for exponential stability with respect to the C^1-norm is optimal. In particular a known weaker sufficient condition for exponential stability with respect to the H^2-norm is not sufficient for the exponential stability with respect to the C^1-norm. Hence, due to the nonlinearity, even in the case of classical solutions, the exponential stability depends strongly on the norm considered. We also give a new sufficient condition for the exponential stability with respect to the W^{2,p}-norm. The methods used are inspired from the theory of the linear time-delay systems and incorporate the characteristic method.
%U http://arxiv.org/abs/1403.1747v1