Erratum to: The Controllability of the Gurtin-Pipkin Equation: A Cosine Operator Approach

Erratum to: The Controllability of the Gurtin-Pipkin Equation: A Cosine Operator Approach Appl Math Optim (2011) 64:467–468 DOI 10.1007/s00245-011-9149-6 ERRATUM Erratum to: The Controllability of the Gurtin-Pipkin Equation: A Cosine Operator Approach Luciano Pandolfi Published online: 20 September 2011 © Springer Science+Business Media, LLC 2011 Erratum to: Appl Math Optim (2005) 52: 143–165 DOI 10.1007/s00245-005-0819-0 −1 ⊥ ⊥ Lemma 18 states that A [R ] ⊆[R ] . Its proof is based on Lemma 17 which ∞ ∞ is not correct since an integral in the (sketched) computations does not cancel out. A proof of Lemma 18 which does not use Lemma 17 is as follows. Using formula (7), the Laplace transform of θ(t) with θ(0) = 0is −1 θ(λ) =−A I − A Du(λ). ˆ (1) b(λ) −t Let u(t ) = u e . For every λ (in a right half-plane) and ξ ⊥ R we have 0 ∞ −1 1 λ 0 =−ξ, θ(λ)= ξ, A I − A Du , ∀u ∈ U. 0 0 1 + λ b(λ) The assumptions on b(t ) imply that this equality can be extended by continuity to λ = 0 and for λ = 0we have ξ, Du = 0 for every u ∈ U . Hence, if ξ ⊥ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Erratum to: The Controllability of the Gurtin-Pipkin Equation: A Cosine Operator Approach

Loading next page...
 
/lp/springer_journal/erratum-to-the-controllability-of-the-gurtin-pipkin-equation-a-cosine-NPsowO8FFK
Publisher
Springer-Verlag
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics; Numerical and Computational Physics; Mathematical Methods in Physics; Systems Theory, Control
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-011-9149-6
Publisher site
See Article on Publisher Site

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial