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arXiv · 1403.1747

Dissipative boundary conditions for nonlinear 1-D hyperbolic systems: sharp conditions through an approach via time-delay systems

Jean-Michel Coron·Hoai-Minh Nguyen
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Abstract

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.

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Jean-Michel Coron, Hoai-Minh Nguyen. 2014-03-07. Dissipative boundary conditions for nonlinear 1-D hyperbolic systems: sharp conditions through an approach via time-delay systems. https://arxiv.org/abs/1403.1747

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