Optimal polynomial decay of functions and operator semigroups

By A. Borichev, Yuri Tomilov. 2009

778 citations recorded by the source corpus.

We characterize the polynomial decay of orbits of Hilbert space C0-semigroups in resolvent terms. We also show that results of the same type for general Banach space semigroups and functions obtained recently in Batty and Duyckaerts (J Evol Eq 8:765–780, 2008) are sharp. This settles a conjecture posed in Batty and Duyckaerts (2008).

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/5c59f14d84c45104f2714e28faf72d30ee55a420

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

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.”
Stability to weakly dissipative Timoshenko systems (2013, methodology): “Firstly, we use a recent result due to Borichev and Tomilov [20] to prove Equation (5.”
Moore-Gibson-Thompson thermoelasticity with two temperatures (2020, methodology): “To obtain a heat conduction theory with delays but without such an xplosive behavior, Quintanilla (2008, 2009) combined the delay paameters of Tzou and Choudhuri with the two-temperatures theory proosed by Chen and Gurtin (1968) , Chen et al. (1968, 1969) , Warren and hen (1973) .”
The stability number of the Timoshenko system with second sound (2012, methodology): “11) On the other hand, to show the polynomial stability we use the result [2].”
Stability of an abstract system of coupled hyperbolic and parabolic equations (2012, background): “Borichev, A., Tomilov, Y.: Optimal polynomial decay of functions and operator semigroups.”
Sharp polynomial decay rates for the damped wave equation on the torus (2012, methodology): “(2-11) Theorem 2.3 and Proposition 2.4 are proved in Part II, as consequences of the characterization of polynomial decay for general semigroups in terms of resolvent estimates given in [Borichev and Tomilov 2010], providing the equivalence between (2-7) and (2-8).”
Optimal rates of decay for operator semigroups on Hilbert spaces (2017, background): “3) without the logarithm as in [12] (but now with asymptotic equivalence rather than unknown constants C, c > 0).”
Fine scales of decay of operator semigroups (2013, background): “2 itself is proved in [17] by means of an auxiliary operator construction.”