| Title:
|
A monotonicity method for solving hyperbolic problems with hysteresis (English) |
| Author:
|
Krejčí, Pavel |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1988 |
| Pages:
|
197-203 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
A version of the Minty-Browder method is used for proving the existence and uniqueness of a weak $\omega$-periodic solution to the equation $u_{tt}\rightarrow \text {div} F(\text {grad } u)= g$ in a bounded domain $\Omega \subset \bold R^N$ with the boundary condition $u=0$ on $\delta \Omega$, where $g$ is a given (generalized) $\omega$-periodic function and $F$ is the Ishlinskii hysteresis operator. () |
| Keyword:
|
quasilinear |
| Keyword:
|
method of Minty-Browder type |
| Keyword:
|
existence |
| Keyword:
|
uniqueness |
| Keyword:
|
weak $\omega$-periodic solution |
| Keyword:
|
vibrating processes |
| Keyword:
|
elasto-plastic solids |
| Keyword:
|
ferromagnetics |
| Keyword:
|
Ishlinskii hysteresis operator |
| Keyword:
|
finite speed of propagation |
| Keyword:
|
sharp estimates |
| Keyword:
|
hysteresis energy losses |
| MSC:
|
35B10 |
| MSC:
|
35B40 |
| MSC:
|
35L70 |
| MSC:
|
74H45 |
| MSC:
|
74H99 |
| idZBL:
|
Zbl 0668.35065 |
| idMR:
|
MR0944783 |
| DOI:
|
10.21136/AM.1988.104302 |
| . |
| Date available:
|
2008-05-20T18:34:36Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104302 |
| . |
| Reference:
|
[1] S. Fučík A. Kufner: Nonlinear differential equations.(Czech). SNTL, Praha, 1978. |
| Reference:
|
[2] P. Krejčí: Hysteresis and periodic solutions to semilinear and quasilinear wave equations.Math. Z. 193 (1986), 247-264. MR 0856153, 10.1007/BF01174335 |
| Reference:
|
[3] P. Krejčí: On Ishlinskii model for non-perfectly elastic bodies.Apl. mat. 33 (1988), No. 2, 133-144. MR 0940712 |
| Reference:
|
[4] A. Kufner O. John S. Fučík: Function spaces.Academia, Praha, 1977. MR 0482102 |
| Reference:
|
[5] J.-L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod, Gauthier-Villars, Paris, 1969. Zbl 0189.40603, MR 0259693 |
| Reference:
|
[6] О. В. Бесов, В П. Ильин С. М. Никольский: Интегральные представления функций и теоремы вложения.Наука, Москва, 1975. Zbl 1231.90252 |
| Reference:
|
[7] А. Ю. Ишлинский: Некоторые применения статистики к описанию законов деформирования тел.Изв. АН СССР, OTH, 1944, Но 9, 583-590. Zbl 0149.19102 |
| Reference:
|
[8] M. А. Красносельский А. В. Покровский: Системы с гистерезисом.Наука, Москва, 1983. Zbl 1229.47001 |
| . |
