文章基本信息

标题：Non-linear damping for scattering-passive systems in the Maxwell class ⁎
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作者：Shantanu Singh ; George Weiss ; Marius Tucsnak 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2020
卷号：53
期号：2
页码：7458-7465
DOI：10.1016/j.ifacol.2020.12.1298
语种：English
出版社：Elsevier
摘要：AbstractWe start from a special class of scattering passive linear infinite-dimensional systems introduced in Staffans and Weiss (SIAM J. Control and Opt., 2012). This class is called the Maxwell class of systems, because it includes the scattering formulation of Maxwell’s equations, as well as various wave and beam equations. We generalize this class by allowing a nonlinear damping term. While the system may have unbounded linear damping (for instance, boundary damping), the nonlinear damping termNis “bounded” in the sense that it defined on the whole state space (but no actual continuity assumption is made onN). We show that this new class of nonlinear infinite dimensional systems is well-posed and scattering passive. Our approach uses the theory of maximal monotone operators and the Crandall-Pazy theorem about nonlinear contraction semigroups, which we apply to a Lax-Phillips type nonlinear semigroup that represents the whole system, with input and output signals.
关键词：KeywordsWell-posed linear systemoperator semigroupLax Phillips semigroupscattering passive systemMaxwell’s equationsmaximal monotone operatorCrandall-Pazy theorem