| Title:
|
On some properties of solutions of transonic potential flow problems (English) |
| Author:
|
Gittel, Hans-Peter |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
5 |
| Year:
|
1989 |
| Pages:
|
402-416 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with solutions of transonic potential flow problems handled in the weak form or as variational inequalities. Using suitable generalized methods, which are well known for elliptic partial differential equations of the second order, some properties of these solutions are derived. A maximum principle, a comparison principle and some conclusions from both ones can be established. (English) |
| Keyword:
|
solutions of transonic potential flow problems |
| Keyword:
|
variational inequalities |
| Keyword:
|
generalized methods |
| Keyword:
|
elliptic partial differential equations of the second order |
| Keyword:
|
maximum principle |
| Keyword:
|
comparison principle |
| Keyword:
|
weak formulation |
| MSC:
|
35Q35 |
| MSC:
|
49S05 |
| MSC:
|
76H05 |
| idZBL:
|
Zbl 0689.76019 |
| idMR:
|
MR1014081 |
| DOI:
|
10.21136/AM.1989.104368 |
| . |
| Date available:
|
2008-05-20T18:37:33Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104368 |
| . |
| Reference:
|
[1] M. Feistauer J. Nečas: On the solvability of transonic potential flow problems.Z. Anal. Anw. 4 (1985), 305-329. MR 0807140, 10.4171/ZAA/155 |
| Reference:
|
[2] M. Feistauer J. Nečas: On the solution of transonic flows with weak shocks.Comment. Math. Univ. Carolinae, 27 (1986), 791 - 804. MR 0874673 |
| Reference:
|
[3] M. Feistauer J. Nečas: Viscosity method in a transonic flow.Comm. Partial Differential, Equations (to appear). MR 0940958 |
| Reference:
|
[4] M. Feistauer J. Nečas: Remarks on the solvability of transonic flow problems.Manuscr. Math. (to appear). MR 0952087 |
| Reference:
|
[5] D. Gilbarg N. S. Trudinger: Elliptic partial differential equations of second order.Springer- Verlag, Berlin, 1977. MR 0473443 |
| Reference:
|
[6] H.-P. Gittel: Studies on transonic flow problems by nonlinear variational inequalities.Z. Anal. Anw., 6 (1987), 449-458. Zbl 0655.76050, MR 0923530, 10.4171/ZAA/263 |
| Reference:
|
[7] L. D. Landau E. M. Lifschitz: Lehrbuch der Theoretischen Physik, Bd. VI: Hydrodynamik.Akademie-Verlag, Berlin, 1966. |
| Reference:
|
[8] C. Morawetz: On a weak solution for a transonic flow problem.Comm. Pure Appl. Math., 38 (1985), 797-818. Zbl 0615.76070, MR 0812348, 10.1002/cpa.3160380610 |
| Reference:
|
[9] J. Nečas J. Mandel M. Feistauer: Entropy regularization of the transonic potential flow problem.Comment. Math. Univ. Carolinae, 25 (1984), 431 - 443. MR 0775562 |
| . |
