Characterization of polynomial decay rate for the solution of linear evolution equation

By Zhuangyi Liu, Bopeng Rao. 2005

353 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/dd3250a278cb4ed71bca6f15ce887b6c80f187cb

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In Control and Systems Engineering

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

Energy decay rate of the thermoelastic Bresse system (2009, methodology): “Our main tools are the frequency domain characterization of exponential decay obtained by Pr¨uss [12] and Huang [6], and of polynomial decay obtained recently by the authors of the present paper [ 10 ].”
Sharp polynomial decay rates for the damped wave equation on the torus (2012, methodology): “In particular, [Bardos et al. 1992], [Liu and Rao 2005], [Burq and Hitrik 2007; Nishiyama 2009] and [Christianson 2007; Schenck 2011] can be seen as counterparts for damped wave equations of the articles [Lebeau 1992], [Haraux 1989a; Jaffard 1990], [Burq and Zworski 2004] and [Anantharaman and…”
Stabilization of multidimensional wave equation with locally boundary fractional dissipation law under geometric conditions (2019, background): “4 of [12] (see also [9, 10, 20]) that we partially recall.”
Bresse system with infinite memories (2015, methodology): “If we consider F1 D F3 D 0 and F2 D t with > 0, we obtain the system obtained by Bresse [3] in 1856, which consists of three coupled wave equations and is more general than the well-known Timoshenko system, where the longitudinal displacement is not considered: l D 0 [4, 5].”
On the time polynomial decay in elastic solids with voids (2008, methodology): “Recently, Z. Liu and B. Rao [ 9 ] and A. Batkai et al. [14] found sufficient conditions to get a polynomial decay of semigroup operators.”
Non-uniform stability for bounded semi-groups on Banach spaces (2008, methodology): “In particular, use of the method devised by Newman [24] and Korevaar [14], as in [4], simplifies the proofs given in [3], [5], [15], [18].”
On the existence of time optimal controls for linear evolution equations (2007, background): “We refer to [12], [16] and the references cited therein for related results in this respect.”
Optimal polynomial decay of functions and operator semigroups (2009, background): “The above applications (mainly in the abstract set-up) motivated a thorough study of the decay rates on ‖T (t)A−1‖ for bounded C0-semigroups (T (t))t≥0 on Banach spaces in [3], [21], and, most recently, in [6].”
Fine scales of decay of operator semigroups (2013, background): “Among them, we would like to mention [9], [16], [19], [21], [22], [53], and especially the very recent paper [4] as samples.”