Article
| Title: | The existence of a periodic solution of a parabolic equation with the Bessel operator (English) |
| Author: | Lauerová, Dana |
| Language: | English |
| Journal: | Aplikace matematiky |
| ISSN: | 0373-6725 |
| Volume: | 29 |
| Issue: | 1 |
| Year: | 1984 |
| Pages: | 40-44 |
| Summary lang: | English |
| Summary lang: | Czech |
| Summary lang: | Russian |
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| Category: | math |
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| Summary: | In this paper, the existence of an $\omega$-periodic weak solution of a parabolic equation (1.1) with the boundary conditions (1.2) and (1.3) is proved. The real functions $f(t,r),h(t),a(t)$ are assumed to be $\omega$-periodic in $t,f\in L_2(S,H),a,h$ such that $a'\in L_\infty (R), h'\in L_\infty (R)$ and they fulfil (3). The solution $u$ belongs to the space $L_2(S,V)\cap L_\infty (S,H)$, has the derivative $u'\in L_2(S,H)$ and satisfies the equations (4.1) and (4.2). In the proof the Faedo-Galerkin method is employed. (English) |
| Keyword: | diffusion |
| Keyword: | Bessel operator |
| Keyword: | periodic solutions |
| Keyword: | existence |
| Keyword: | weak solution |
| MSC: | 35B10 |
| MSC: | 35D05 |
| MSC: | 35K20 |
| idZBL: | Zbl 0552.35042 |
| idMR: | MR0729951 |
| DOI: | 10.21136/AM.1984.104066 |
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| Date available: | 2008-05-20T18:23:58Z |
| Last updated: | 2020-07-28 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/104066 |
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| Reference: | [1] R. S. Minasjan: On one problem of the periodic heat flow in the infinite cylinder.Dokl. Akad. Nauk Arm. SSR 48 (1969). MR 0241828 |
| Reference: | [2] H. Triebel: Höhere Analysis.VEB Berlin 1972. Zbl 0257.47001 |
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