SECOND ORDER SYSTEMS ON HILBERT SPACES WITH NONLINEAR DAMPING

被引：1

作者：

Singh, Shantanu ^{[1
]}

Weiss, George ^{[1
]}

机构：

[1] Tel Aviv Univ, Sch Elect Engn, IL-69978 Ramat Aviv, Israel

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2023年 / 61卷 / 04期

基金：

以色列科学基金会;

关键词：

well-posed linear system; operator semigroup; Lax-Phillips semigroup; scattering passive system; maximal monotone operator; Minty's theorem; Rockafellar's theorem; Crandall-Pazy theorem; DIMENSIONAL LINEAR-SYSTEMS; WELL-POSEDNESS; WAVE-EQUATION; THIN AIR; PART II; STABILIZATION; DISSIPATION; OPERATORS; BEAM;

D O I：

10.1137/22M154199X

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We investigate a special class of nonlinear infinite dimensional systems. These systems are obtained by modifying the second order differential equation that is part of the description of conservative linear systems "out of thin air" introduced by Tucsnak and Weiss in 2003. The modified differential equation contains a new nonlinear damping term that is maximal monotone and possibly set-valued. We show that this new class of nonlinear infinite dimensional systems is incrementally scattering passive (hence well-posed). 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. We illustrate our result on the n-dimensional wave equation.

引用

页码：2630 / 2654

页数：25

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