| Title:
|
On a conjugate semi-variational method for parabolic equations (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
18 |
| Issue:
|
6 |
| Year:
|
1973 |
| Pages:
|
434-444 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Initial-boundary value problems for parabolic equations of the second order can be formulated, like the elliptic problems, also by means of conjugate variables, i.e. in terms of the cogradient vector function.
The conjugate problem is shown to belong to a class of abstract parabolic equations with two positive operators, which have been analysed in a previous author's paper. The first and second semi-variational approximations to the solution of the conjugate problem are presented together with some error estimates. () |
| MSC:
|
35B45 |
| MSC:
|
35K20 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0278.35048 |
| idMR:
|
MR0404858 |
| DOI:
|
10.21136/AM.1973.103499 |
| . |
| Date available:
|
2008-05-20T17:57:31Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103499 |
| . |
| Reference:
|
[1] M. A. Biot: Thermoelasticity and irreversible thermodynamics.J. Appl. Phys. 27 (1956), 240-253. Zbl 0071.41204, MR 0077441, 10.1063/1.1722351 |
| Reference:
|
[2] R. A. Schapery : Irreversible thermodynamics and variational principles with applications to viscoelasticity.Aeronaut. Res. Labs. Wright-Patterson Air Force Base, Ohio (1962). |
| Reference:
|
[3] J. Douglas Jг. T. Dupont: Galerkin methods for parabolic equations.SIAM J. Numer. Anal. 7 (1970), 4, 575-626. MR 0277126, 10.1137/0707048 |
| Reference:
|
[4] I. Hlaváček: On a semi-variational method for parabolic equations.I. Aplikace matematiky 17 (1972), 5, 327-351, II. Aplikace matematiky 18 (1973), 1, 43-64. MR 0314285 |
| Reference:
|
[5] J. P. Aubin H. G. Burchard: Some aspects of the method of the hypercircle applied to elliptic variational problems.Numer. Sol. of Part. Dif. Eqs-II, Synspade 1970, 1 - 67. MR 0285136 |
| Reference:
|
[6] I. Hlaváček: Variational principles for parabolic equations.Aplikace matematiky 14 (1969), 4, 278-297. MR 0255988 |
| Reference:
|
[7] J. L. Lions: Equations differentielles operationelles et problèmes aux limites.Grundlehren Math. Wiss., Bd 111, Springer 1961. MR 0153974 |
| . |
