| Title:
|
Convergence of Rothe's method in Hölder spaces (English) |
| Author:
|
Kikuchi, N. |
| Author:
|
Kačur, J. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
48 |
| Issue:
|
5 |
| Year:
|
2003 |
| Pages:
|
353-365 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The convergence of Rothe’s method in Hölder spaces is discussed. The obtained results are based on uniform boundedness of Rothe’s approximate solutions in Hölder spaces recently achieved by the first author. The convergence and its rate are derived inside a parabolic cylinder assuming an additional compatibility conditions. (English) |
| Keyword:
|
Rothe’s method |
| Keyword:
|
method of lines |
| Keyword:
|
convergence of Rothe’s method |
| MSC:
|
35B50 |
| MSC:
|
35K20 |
| MSC:
|
46E35 |
| MSC:
|
65M12 |
| MSC:
|
65M20 |
| MSC:
|
65M40 |
| idZBL:
|
Zbl 1099.65079 |
| idMR:
|
MR2008889 |
| DOI:
|
10.1023/B:APOM.0000024481.01947.da |
| . |
| Date available:
|
2009-09-22T18:14:20Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134535 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
[9] V. Pluschke: $L_{\infty }$-estimates and uniform convergence of Rothe’s method for quasilinear parabolic differential equations.Methoden Verfahren Math. Phys. Vol 37, K. Kleinman et al. (eds.), Peter Lang-Verlag, 1991, pp. 187–199. MR 1215747 |
| Reference:
|
[10] V. Pluschke: Local solutions to quasilinear parabolic equations without growth restrictions.Z. Anal. Anwendungen 15 (1996), 375–396. Zbl 0851.35051, MR 1394434, 10.4171/ZAA/706 |
| Reference:
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| Reference:
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| Reference:
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| . |
