On some properties of solutions of transonic potential flow problems

Hans-Peter Gittel

Aplikace matematiky (1989)

  • Volume: 34, Issue: 5, page 402-416
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Gittel, Hans-Peter. "On some properties of solutions of transonic potential flow problems." Aplikace matematiky 34.5 (1989): 402-416. <http://eudml.org/doc/15594>.

@article{Gittel1989,
abstract = {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.},
author = {Gittel, Hans-Peter},
journal = {Aplikace matematiky},
keywords = {solutions of transonic potential flow problems; variational inequalities; generalized methods; elliptic partial differential equations of the second order; maximum principle; comparison principle; weak formulation; solutions of transonic potential flow problems; variational inequalities; generalized methods; elliptic partial differential equations of the second order; maximum principle; comparison principle},
language = {eng},
number = {5},
pages = {402-416},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some properties of solutions of transonic potential flow problems},
url = {http://eudml.org/doc/15594},
volume = {34},
year = {1989},
}

TY - JOUR
AU - Gittel, Hans-Peter
TI - On some properties of solutions of transonic potential flow problems
JO - Aplikace matematiky
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 5
SP - 402
EP - 416
AB - 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.
LA - eng
KW - solutions of transonic potential flow problems; variational inequalities; generalized methods; elliptic partial differential equations of the second order; maximum principle; comparison principle; weak formulation; solutions of transonic potential flow problems; variational inequalities; generalized methods; elliptic partial differential equations of the second order; maximum principle; comparison principle
UR - http://eudml.org/doc/15594
ER -

References

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  1. M. Feistauer J. Nečas, On the solvability of transonic potential flow problems, Z. Anal. Anw. 4 (1985), 305-329. (1985) MR0807140
  2. M. Feistauer J. Nečas, On the solution of transonic flows with weak shocks, Comment. Math. Univ. Carolinae, 27 (1986), 791 - 804. (1986) MR0874673
  3. M. Feistauer J. Nečas, Viscosity method in a transonic flow, Comm. Partial Differential, Equations (to appear). MR0940958
  4. M. Feistauer J. Nečas, Remarks on the solvability of transonic flow problems, Manuscr. Math. (to appear). MR0952087
  5. D. Gilbarg N. S. Trudinger, Elliptic partial differential equations of second order, Springer- Verlag, Berlin, 1977. (1977) MR0473443
  6. H.-P. Gittel, Studies on transonic flow problems by nonlinear variational inequalities, Z. Anal. Anw., 6 (1987), 449-458. (1987) Zbl0655.76050MR0923530
  7. L. D. Landau E. M. Lifschitz, Lehrbuch der Theoretischen Physik, Bd. VI: Hydrodynamik, Akademie-Verlag, Berlin, 1966. (1966) 
  8. C. Morawetz, 10.1002/cpa.3160380610, Comm. Pure Appl. Math., 38 (1985), 797-818. (1985) Zbl0615.76070MR0812348DOI10.1002/cpa.3160380610
  9. J. Nečas J. Mandel M. Feistauer, Entropy regularization of the transonic potential flow problem, Comment. Math. Univ. Carolinae, 25 (1984), 431 - 443. (1984) MR0775562

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