A principle of linearization in theory of stability of solutions of variational inequalities

Jiří Neustupa

Mathematica Bohemica (1995)

  • Volume: 120, Issue: 4, page 337-345
  • ISSN: 0862-7959

Abstract

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It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.

How to cite

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Neustupa, Jiří. "A principle of linearization in theory of stability of solutions of variational inequalities." Mathematica Bohemica 120.4 (1995): 337-345. <http://eudml.org/doc/247780>.

@article{Neustupa1995,
abstract = {It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.},
author = {Neustupa, Jiří},
journal = {Mathematica Bohemica},
keywords = {linearization; stability; variational inequality; linearization; stability; variational inequality},
language = {eng},
number = {4},
pages = {337-345},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A principle of linearization in theory of stability of solutions of variational inequalities},
url = {http://eudml.org/doc/247780},
volume = {120},
year = {1995},
}

TY - JOUR
AU - Neustupa, Jiří
TI - A principle of linearization in theory of stability of solutions of variational inequalities
JO - Mathematica Bohemica
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 120
IS - 4
SP - 337
EP - 345
AB - It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.
LA - eng
KW - linearization; stability; variational inequality; linearization; stability; variational inequality
UR - http://eudml.org/doc/247780
ER -

References

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  1. J. P. Aubin A. Cellina, Differential Inclusions, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1984. (1984) MR0755330
  2. H.Brézis, Problèmes unilatéraux, J. Math. Pures Appl. 51 (1972), 1-168. (1972) Zbl0264.73015MR0428137
  3. P. Drábek M. Kučera, Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions, Czech. Math. J. 36 (111) (1986), 116-130. (1986) MR0822872
  4. P. Drábek M. Kučera, 10.1016/0362-546X(88)90051-X, Nonlinear Analysis, Theory, Methods & Applications 12 (1988), no. 11, 1173-1192. (1988) MR0969497DOI10.1016/0362-546X(88)90051-X
  5. H. Gajewski K. Gröger K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974. (1974) MR0636412
  6. J. Neustupa, The linearized uniform asymptotic stability of evolution differential equations, Czech. Math. J. 34 (109) (1984), 257-284. (1984) Zbl0599.34081MR0743491
  7. M. Kučera J. Neustupa, Destabilizing effect of unilateral conditions in reaction-diffusion systems, Commentationes Math. Univ. Carolinae 27 (1986), no. 1, 171-187. (1986) MR0843429
  8. P. Quittner, 10.1007/BF01446434, Math. Ann. vol 283 (1989), 257-270. (1989) MR0980597DOI10.1007/BF01446434

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