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Mathematics > Analysis of PDEs

arXiv:1403.1747 (math)
[Submitted on 7 Mar 2014]

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

Authors:Jean-Michel Coron (LJLL), Hoai-Minh Nguyen (EPFL)
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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.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1403.1747 [math.AP]
  (or arXiv:1403.1747v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1403.1747

Submission history

From: Jean-Michel Coron [view email] [via CCSD proxy]
[v1] Fri, 7 Mar 2014 13:29:56 UTC (64 KB)
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