Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems

Coron, Jean-MichelNguyên, Hoài-Minh2015-09-282015-09-282015-09-28201510.1137/140976625https://infoscience.epfl.ch/handle/20.500.14299/119130WOS:000357408600020We analyze dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a known 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,W-p-norm. The methods used are inspired from the theory of the linear time-delay systems and incorporate the characteristic method.hyperbolic systemsdissipative boundary conditionsexponential stabilitytime-delay systemsnonlinearitiesDissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systemstext::journal::journal article::research article