New classes of analytic and Gevrey semigroups and applications

Angelo Favini; Roberto Triggiani

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 1, page 29-34
  • ISSN: 1120-6330

Abstract

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We consider the operator - A + i ⁢ B on a complex Hilbert space, where A is positive self-adjoint and B is self-adjoint, and where, moreover, « B is comparable to A α , α ≥ 1 », in a technical sense. Two applications are given.

How to cite

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Favini, Angelo, and Triggiani, Roberto. "New classes of analytic and Gevrey semigroups and applications." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.1 (1993): 29-34. <http://eudml.org/doc/244071>.

@article{Favini1993,
abstract = {We consider the operator \( -A + iB \) on a complex Hilbert space, where \( A \) is positive self-adjoint and \( B \) is self-adjoint, and where, moreover, «\( B \) is comparable to \( A^\{\alpha\} \), \( \alpha \ge 1 \)», in a technical sense. Two applications are given.},
author = {Favini, Angelo, Triggiani, Roberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Analytic semigroups; Gevrey class semigroups; Optimal control problems; Cauchy problems; analytic semigroups; optimal control problems},
language = {eng},
month = {3},
number = {1},
pages = {29-34},
publisher = {Accademia Nazionale dei Lincei},
title = {New classes of analytic and Gevrey semigroups and applications},
url = {http://eudml.org/doc/244071},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Favini, Angelo
AU - Triggiani, Roberto
TI - New classes of analytic and Gevrey semigroups and applications
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/3//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 1
SP - 29
EP - 34
AB - We consider the operator \( -A + iB \) on a complex Hilbert space, where \( A \) is positive self-adjoint and \( B \) is self-adjoint, and where, moreover, «\( B \) is comparable to \( A^{\alpha} \), \( \alpha \ge 1 \)», in a technical sense. Two applications are given.
LA - eng
KW - Analytic semigroups; Gevrey class semigroups; Optimal control problems; Cauchy problems; analytic semigroups; optimal control problems
UR - http://eudml.org/doc/244071
ER -

References

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  1. CHEN, S. - TRIGGIANI, R., Proof of two conjectures by G. Chen and D. L. Russell on structural damping for elastic systems. Proceedings of Conference on Approximation and Optimization held at the University of Havana (Cuba, January 1987). Lecture notes in mathematics, n. 1354, Springer-Verlag, 1988, 234-256. Zbl0669.34015MR996678DOI10.1007/BFb0089601
  2. FAVINI, A. - YAGI, A., Multivalued linear operator and degenerate evolution equations. Ann. Mat. Pura Appl., to appear. Zbl0786.47037MR1219605DOI10.1007/BF01759029
  3. FLANDOLI, F. - LASIECKA, I. - TRIGGIANI, R., Algebraic Riccati equations with non-smoothing observation arising in hyperbolic and Euler-Bemoulli equations. Ann. Mat. Pura Appl., vol. 153, 1988, 307-382. Zbl0674.49004MR1008349DOI10.1007/BF01762397
  4. KATO, T., Perturbation theory for linear operators. Springer-Verlag, 1966. Zbl0836.47009MR203473
  5. KREIN, S. G., Linear differential equations in Banach space. Translations of Math. Monographs, American Math. Soc., vol. 29, 1971. Zbl0229.34050MR342804
  6. LASIECKA, I. - TRIGGIANI, R., Riccati equations arising from systems with unbounded input-solution operator: applications to boundary control problems for wave and plate problems. J. of Nonlinear Analysis, to appear. Zbl0798.49007
  7. PAZY, A., Semigroups of operators and applications to partial differential equations. Springer-Verlag, New York1983. Zbl0516.47023MR710486DOI10.1007/978-1-4612-5561-1
  8. TAIRA, K., The theory of semigroups with weak singularity and its applications to partial differential equations. Tsakuba J. Math., 13, 1989, 513-562. Zbl0695.47031MR1030233
  9. TAYLOR, S., Gevrey class semigroups. Ph. D. thesis, School of Mathematics, University of Minnesota, 1989, Chapter 1. 

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