Henrot, Antoine; Pierre, Michel Un problème inverse en formage des métaux liquides. (An inverse problem for liquid metals forming). (French) Zbl 0672.65101 RAIRO, Modélisation Math. Anal. Numér. 23, No. 1, 155-177 (1989). The authors consider the problem of a jet of liquid metal falling under the influence of gravity, and subject to an external magnetic field. They show that if the shape of the jet is known, then, provided that the boundary of the section is an analytic curve, it is possible to determine the magnetic field in the neighbourhood of the boundary. The analysis is applied to the case where the boundary of a section is a trochoidal curve. The possibility of finding the magnetic field everywhere is also discussed. Reviewer: Ll.G.Chambers Cited in 13 Documents MSC: 65Z05 Applications to the sciences 35R30 Inverse problems for PDEs 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 76W05 Magnetohydrodynamics and electrohydrodynamics 35J55 Systems of elliptic equations, boundary value problems (MSC2000) Keywords:inverse problem; liquid metals forming; jet of liquid metal; gravity; external magnetic field PDF BibTeX XML Cite \textit{A. Henrot} and \textit{M. Pierre}, RAIRO, Modélisation Math. Anal. Numér. 23, No. 1, 155--177 (1989; Zbl 0672.65101) Full Text: DOI EuDML References: [1] BERKOWITZ J., FRIEDRICHS V. O., GOERTZEL H., GRAD H., KILLEEN J. et ROBIN E., 1958, Cusped geometries, Proc. Second Int. Conf. on Peaceful Uses of Atomic Energy, U.N. Geneva, vol. 31, p. 171. [2] BRANCHER J. P. et SERO-GUILLAUME O., Sur l’équilibre des liquides magnétiques, Application à la magnétostatique (J.M.T.A., vol. 2, n^\circ 2, 1983, p. 265-283). Zbl0539.76119 · Zbl 0539.76119 [3] BRANCHER J. P., ETAY J., SERO-GUILLAUME O., Formage d’une lame, (J.M.T.A., vol. 2, n^\circ 6, 1983, p. 976-989). Zbl0564.76119 · Zbl 0564.76119 [4] DIEUDONNE, Calcul infinitésimal, p. 317. Zbl0155.10001 · Zbl 0155.10001 [5] ETAY J., Le formage électromagnétique des métaux liquides. Aspects expérimentaux et théoriques (Thèse Docteur-Ingénieur, U.S.M.G., I.N.P.G., 1982). [6] MORREY C. B. Jr., Multiple integrals in the Calculus of Variations, Springer Verlag (1966). Zbl0142.38701 MR202511 · Zbl 0142.38701 [7] POMMERENKE Chr., Univalent functions, Studia Mathematica, Vandenhoeck & Ruprecht, Göttingen (1975). Zbl0298.30014 MR507768 · Zbl 0298.30014 [8] SHERCLIFF J. A., Magnetic shaping of molten metal columns (Proc. R. Soc. Lond. A 375, p. 455-473, 1981). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.