Erratum to: Decay Rates to Equilibrium for Nonlinear Plate Equations with Degenerate, Geometrically-Constrained Damping

Erratum to: Decay Rates to Equilibrium for Nonlinear Plate Equations with Degenerate,... Appl Math Optim (2014) 70:565–566 DOI 10.1007/s00245-014-9275-z ERRATUM Erratum to: Decay Rates to Equilibrium for Nonlinear Plate Equations with Degenerate, Geometrically-Constrained Damping Pelin G. Geredeli · Justin T. Webster Published online: 11 October 2014 © Springer Science+Business Media New York 2014 Erratum to: Appl Math Optim (2013) 68: 361–390 DOI 10.1007/s00245-013-9210-8 It was brought to our attention that line 15 on page 374—which claims u = 0 in  × —is unclear. Upon further inspection, this statement should differentiate between two cases: (a) p(x) = 0on  and (b) p(x) = 0(takenin the L () sense). Case (a): As argued in the treatment, the application of Holmgren’s theorem gives u = 0on ω ×. The desired final conclusion follows by inserting this information into Berger’s equation (by assumption, no longer containing the damping term d(x)g(u )), and then employing Kim’s unique continuation result Theorem 3.1. Case (b): One reaches a contradiction with the additional mild assumption that there exists a set of positive measure U ⊂ ω so that p(x) = 0on U. Thus Theorem 3.2, and consequently Theorems 2.5, 2.6 (Main Results), remain valid when (a) p(x) ≡ 0, and when (b) p(x) ∈ L () is non-trivial, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Erratum to: Decay Rates to Equilibrium for Nonlinear Plate Equations with Degenerate, Geometrically-Constrained Damping

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9275-z
Publisher site
See Article on Publisher Site

Abstract

Appl Math Optim (2014) 70:565–566 DOI 10.1007/s00245-014-9275-z ERRATUM Erratum to: Decay Rates to Equilibrium for Nonlinear Plate Equations with Degenerate, Geometrically-Constrained Damping Pelin G. Geredeli · Justin T. Webster Published online: 11 October 2014 © Springer Science+Business Media New York 2014 Erratum to: Appl Math Optim (2013) 68: 361–390 DOI 10.1007/s00245-013-9210-8 It was brought to our attention that line 15 on page 374—which claims u = 0 in  × —is unclear. Upon further inspection, this statement should differentiate between two cases: (a) p(x) = 0on  and (b) p(x) = 0(takenin the L () sense). Case (a): As argued in the treatment, the application of Holmgren’s theorem gives u = 0on ω ×. The desired final conclusion follows by inserting this information into Berger’s equation (by assumption, no longer containing the damping term d(x)g(u )), and then employing Kim’s unique continuation result Theorem 3.1. Case (b): One reaches a contradiction with the additional mild assumption that there exists a set of positive measure U ⊂ ω so that p(x) = 0on U. Thus Theorem 3.2, and consequently Theorems 2.5, 2.6 (Main Results), remain valid when (a) p(x) ≡ 0, and when (b) p(x) ∈ L () is non-trivial,

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Dec 1, 2014

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