| Title:
|
A study of an operator arising in the theory of circular plates (English) |
| Author:
|
Herrmann, Leopold |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
5 |
| Year:
|
1988 |
| Pages:
|
337-353 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The operator $L_0:D_{L_0}\subset H \rightarrow H$, $L_0u = \frac 1r \frac d {dr} \left\{r \frac d{dr}\left[\frac 1r \frac d{dr}\left(r \frac {du}{dr}\right)\right] \right\}$, $D_{L_0}= \{u \in C^4 ([0,R]), u'(0)=u''''(0)=0, u(R)=u'(R)=0\}$, $H=L_{2,r}(0,R)$ is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on $L_0$ (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types $L_0u=g$ and $u_{tt}+L_0u=g$, respectively. (English) |
| Keyword:
|
positive definite |
| Keyword:
|
compact resolvent |
| Keyword:
|
Fourier method |
| Keyword:
|
existence theorems |
| Keyword:
|
static |
| Keyword:
|
transverse static deflection |
| Keyword:
|
transverse vibration |
| Keyword:
|
thin homogeneous elastic plate |
| Keyword:
|
transverse load |
| Keyword:
|
dynamic problems |
| Keyword:
|
circular plates theory |
| MSC:
|
34B20 |
| MSC:
|
35C10 |
| MSC:
|
47B25 |
| MSC:
|
47E05 |
| MSC:
|
73K12 |
| MSC:
|
74H45 |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 0658.73037 |
| idMR:
|
MR0961312 |
| DOI:
|
10.21136/AM.1988.104315 |
| . |
| Date available:
|
2008-05-20T18:35:09Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104315 |
| . |
| Reference:
|
[1] R. A. Adams: Sobolev spaces.Academic Press 1975. Zbl 0314.46030, MR 0450957 |
| Reference:
|
[2] B. M. Budak A. A. Samarskii A. N. Tikhonov: A collection of problems on mathematical physics.International series of monographs in pure and applied mathematics 52, Pergamon Press, Oxford 1964. (Russian: Izd. Nauka, Moscow 1980, 3rd ed.). MR 0592954 |
| Reference:
|
[3] A. Erdélyi, at.: Higher transcendental functions.Vol 2. McGraw Hill 1953. |
| Reference:
|
[4] W. G. Faris: Self-adjoint operators.Lecture Notes in Mathematics 433, Springer-Verlag 1975. Zbl 0317.47016, MR 0467348 |
| Reference:
|
[5] P. Hartman: Ordinary differential equations.J. Wiley and Sons 1964. Zbl 0125.32102, MR 0171038 |
| Reference:
|
[6] E. Jahnke F. Emde: Tables of functions.Dover Publ. 1945 (4th ed.). MR 0015900 |
| Reference:
|
[7] W. Magnus F. Oberhettinger: Formeln und Sätze für die speziellen Funktionen der mathematischen Physik.Springer-Verlag 1948 (2nd ed.). MR 0025629 |
| Reference:
|
[8] D. E. Mc Farland B. L. Smith W. D. Bernhart: Analysis of plates.Spartan Books 1972. |
| Reference:
|
[9] S. G. Mikhlin: Linear partial differential equations.(Russian.) Vysš. škola, Moscow 1977. MR 0510535 |
| Reference:
|
[10] S. Timoshenko D. H. Young W. Weaver, Jr.: Vibrations problems in engineering.John Wiley and Sons 1974 (4th ed.). (Russian: Mashinostrojenije, Moscow 1985.) |
| Reference:
|
[11] S. Timoshenko S. Woinowski-Krieger: Theory of plates and shells.McGraw Hill 1959. |
| Reference:
|
[12] O. Vejvoda, al.: Partial differential equations: time-periodic solutions.Martinus Nijhoff 1982. Zbl 0501.35001 |
| Reference:
|
[13J G. N. Watson: A treatise on the theory of Bessel functions.Cambridge Univ. Press 1958 (2nd ed.). MR 1349110 |
| Reference:
|
[14] J. Weidmann: Linear operators in Hilbert spaces.Graduate texts in Mathematics 68, Springer-Verlag 1980. Zbl 0434.47001, MR 0566954 |
| . |
