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

We 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.


Published in:
Siam Journal on Mathematical Analysis, 47, 3, 2220-2240
Year:
2015
Publisher:
Philadelphia, Society for Industrial and Applied Mathematics
ISSN:
0036-1410
Keywords:
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 Record created 2015-09-28, last modified 2018-03-17

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