| Title:
|
An extension of Rothe's method to non-cylindrical domains (English) |
| Author:
|
Kuliev, Komil |
| Author:
|
Persson, Lars-Erik |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
52 |
| Issue:
|
5 |
| Year:
|
2007 |
| Pages:
|
365-389 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper Rothe’s classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied. (English) |
| Keyword:
|
parabolic PDE |
| Keyword:
|
numerical method |
| Keyword:
|
time-discretization |
| Keyword:
|
method of lines |
| Keyword:
|
Rothe’s method |
| MSC:
|
35K20 |
| MSC:
|
65M20 |
| MSC:
|
65N40 |
| idZBL:
|
Zbl 1164.65463 |
| idMR:
|
MR2342595 |
| DOI:
|
10.1007/s10492-007-0021-6 |
| . |
| Date available:
|
2009-09-22T18:30:37Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134683 |
| . |
| Reference:
|
[1] J. Dasht, J. Engström, A. Kufner, and L.-E. Persson: Rothe’s method for parabolic equations on non-cylindrical domains.Advances in Algebra and Analysis 1 (2006), 1–22. MR 2294649 |
| Reference:
|
[2] S. Fučík, A. Kufner: Nonlinear Differential Equations.Elsevier, Amsterdam-Oxford-New York, 1980. MR 0558764 |
| Reference:
|
[3] J. Kačur: Method of Rothe in Evolution Equations.Teubner, Leipzig, 1985. MR 0834176 |
| Reference:
|
[4] A. Kufner, O. John, and S. Fučík: Function Spaces.Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1977. MR 0482102 |
| Reference:
|
[5] K. Rektorys: The Method of Discretization in Time and Partial Differential Equations.D. Reidel, Dordrecht-Boston-London, 1982, pp. . Zbl 0522.65059, MR 0689712 |
| Reference:
|
[6] K. Rektorys: On application of direct variational methods to the solution of parabolic boundary value problems of arbitrary order in space variables.Czech. Math. J. 21 (1971), 318–339. MR 0298237 |
| Reference:
|
[7] K. Rektorys: Variational Methods in Mathematics, Science and Engineering.D. Reidel, Dordrecht-Boston-London, 1980. Zbl 0481.49002, MR 0596582 |
| . |
