Fabrie, Pierre; Gallouët, Thierry Modeling wells in porous media flow. (English) Zbl 1018.76044 Math. Models Methods Appl. Sci. 10, No. 5, 673-709 (2000). Summary: We prove the existence of weak solutions for mathematical models of miscible and immiscible flow through porous medium. An important difficulty comes from the modelization of the wells, which does not allow us to use classical variational formulations of the equations. Cited in 34 Documents MSC: 76S05 Flows in porous media; filtration; seepage 35Q35 PDEs in connection with fluid mechanics Keywords:miscible flow; existence; weak solutions; immiscible flow; porous medium PDFBibTeX XMLCite \textit{P. Fabrie} and \textit{T. Gallouët}, Math. Models Methods Appl. Sci. 10, No. 5, 673--709 (2000; Zbl 1018.76044) Full Text: DOI References: [1] DOI: 10.1007/BF01773387 · Zbl 0552.76075 · doi:10.1007/BF01773387 [2] Alt H. W., Ann. Scuola Norm. Sup. Pisa 12 pp 335– (1985) [3] DOI: 10.1016/0022-1236(89)90005-0 · Zbl 0707.35060 · doi:10.1016/0022-1236(89)90005-0 [4] DOI: 10.1007/BF01442860 · Zbl 0646.35024 · doi:10.1007/BF01442860 [5] Meyers N. G., Ann. SC. Norm. Sup. Pisa 17 pp 189– (1963) [6] Prignet A., Rend. Mat. Appl. 15 pp 321– (1995) [7] DOI: 10.5802/afst.867 · Zbl 0895.35103 · doi:10.5802/afst.867 [8] Simon J., Boll. Un. Mat. Ital. 5 pp 501– (1979) [9] DOI: 10.1007/BF01762360 · Zbl 0629.46031 · doi:10.1007/BF01762360 [10] DOI: 10.5802/aif.204 · Zbl 0151.15401 · doi:10.5802/aif.204 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.