Pasa, Gelu I. An existence theorem for a control problem in oil recovery. (English) Zbl 0883.76083 Numer. Funct. Anal. Optimization 17, No. 9-10, 911-923 (1996). Summary: We study a Sturm-Liouville system, arising from the stability of interfaces in secondary recovery process: the oil is obtained from a porous medium by displacing it with a second fluid (water). A polymer solute contained in an intermediate region (between water and oil) is used to minimize the “fingering” phenomenon (the instability of interfaces). The eigenvalues of the above system are the growth constants (in time) of the perturbations. The growth constants may be controlled by the viscosity in the intermediate region. An existence theorem for an optimal viscosity in the intermediate region is given, which allows us to minimize the maximum growth constant. The Rayleigh’s quotient and the properties of the weakly continuous functionals on a bounded domain of a Hilbert space are used. A characterization is given for the domain of the wavenumbers for which we have only positive growth constants. Cited in 2 Documents MSC: 76S05 Flows in porous media; filtration; seepage 35Q35 PDEs in connection with fluid mechanics 86A20 Potentials, prospecting Keywords:fingering phenomenon; Sturm-Liouville system; stability of interfaces; eigenvalues; optimal viscosity; Rayleigh’s quotient; weakly continuous functionals; Hilbert space PDF BibTeX XML Cite \textit{G. I. Pasa}, Numer. Funct. Anal. Optim. 17, No. 9--10, 911--923 (1996; Zbl 0883.76083) Full Text: DOI OpenURL References: [1] DOI: 10.1098/rspa.1958.0085 · Zbl 0086.41603 [2] Chouke R.L, Trans Aime 216 pp 188– (1959) [3] DOI: 10.1137/0143007 · Zbl 0514.76090 [4] DOI: 10.1016/0020-7225(92)90049-M · Zbl 0825.76233 [5] Pasa G.I, Rev. Roum. Mec. Appl 39 pp 72– (1994) [6] Pasa G.I, A numerical characterization of the growth constant in oil recovery (1994) [7] Cea J, Optimization - Theorie et algorithmes (1971) [8] Courant, R and Hilbert, D. 1965. ”Method of Mathematical Physics”. New York: Interscience Publishers, Inc. · JFM 57.0245.01 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.