Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems
Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems
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DOI：
10.1137/140976625
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发表时间：
2014-03
期刊：
影响因子：
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通讯作者：
J. Coron;Hoai-Minh Nguyen
中科院分区：
文献类型：
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作者：
J. Coron;Hoai-Minh Nguyen
研究一维非线性双曲型系统的耗散边界条件。我们证明了一个已知的关于H^2$范数的指数稳定性的充分条件并不足以证明关于C^1$范数的指数稳定性。因此，由于非线性，即使在经典解的情况下，指数稳定性强烈地依赖于所考虑的范数。给出了关于W^{2，p}$-范数的指数稳定性的一个新的充分条件。所采用的方法受到线性时滞系统理论的启发，并结合了特征方法。
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 $W^{2,p}$-norm. The methods used are inspired from the theory of the linear time-delay systems and incorporate the characteristic method.