| Title:
|
A principle of linearization in theory of stability of solutions of variational inequalities (English) |
| Author:
|
Neustupa, Jiří |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
337-345 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
linearization |
| Keyword:
|
stability |
| Keyword:
|
variational inequality |
| MSC:
|
34D05 |
| MSC:
|
34G20 |
| MSC:
|
34G99 |
| MSC:
|
47H19 |
| MSC:
|
47J20 |
| MSC:
|
47N20 |
| MSC:
|
49J40 |
| MSC:
|
58E35 |
| idZBL:
|
Zbl 0847.34057 |
| idMR:
|
MR1415082 |
| DOI:
|
10.21136/MB.1995.126091 |
| . |
| Date available:
|
2009-09-24T21:12:42Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126091 |
| . |
| Reference:
|
[1] J. P. Aubin A. Cellina: Differential Inclusions.Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1984. MR 0755330 |
| Reference:
|
[2] H.Brézis: Problèmes unilatéraux.J. Math. Pures Appl. 51 (1972), 1-168. Zbl 0264.73015, MR 0428137 |
| Reference:
|
[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. MR 0822872 |
| Reference:
|
[4] P. Drábek M. Kučera: Reaction-diffusion systems: Destabilizing effect of unilateral conditions.Nonlinear Analysis, Theory, Methods & Applications 12 (1988), no. 11, 1173-1192. MR 0969497, 10.1016/0362-546X(88)90051-X |
| Reference:
|
[5] H. Gajewski K. Gröger K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.Akademie-Verlag, Berlin, 1974. MR 0636412 |
| Reference:
|
[6] J. Neustupa: The linearized uniform asymptotic stability of evolution differential equations.Czech. Math. J. 34 (109) (1984), 257-284. Zbl 0599.34081, MR 0743491 |
| Reference:
|
[7] M. Kučera J. Neustupa: Destabilizing effect of unilateral conditions in reaction-diffusion systems.Commentationes Math. Univ. Carolinae 27 (1986), no. 1, 171-187. MR 0843429 |
| Reference:
|
[8] P. Quittner: On the principle of linearized stability for variational inequalities.Math. Ann. vol 283 (1989), 257-270. MR 0980597, 10.1007/BF01446434 |
| . |
