Article PDF
Avoid common mistakes on your manuscript.
References
Saffman P. G. andTaylor G. I., “The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid,” Proc. Roy. Soc. London. Ser. A,245, 312–329 (1958).
Wooding R. A. andMorel-Seytoux H. J., “Multiphase flow through porous media,” Ann. Rew. Fluid Mech.,8, 233–274 (1976).
Otto F., Stability Investigation of Planar Solutions of Buckley-Leverett Equation, Sonderforchungbereich 256 [Preprint; No. 345] (1995).
Kruzhkov S. I., “First order quasilinear equations in several independent variables,” Mat. Sb.,81, No. 2, 228–255 (1970).
Panov E. Yu., “On a sequence of measure-valued solutions to a first order quasilinear equation,” Mat. Sb.,185, 87–106 (1994).
Otto F., First Order Equations with Boundary Conditions, Sonderforchungbereich 256 [Preprint; No. 234] (1992).
Tartar L., “The compensated compactness method applied to systems of conservation laws,” in: Systems of Nonlinear Partial Differential Equations, Reidel Publ. Comp., Dordrecht, Boston, and Massachusetts, 1983, pp. 263–285 (NATO Adv. Sci. Inst. Ser. C.,111).
Perna R. J. Di., “Measure-valued solutions to conservation laws,” Arch. Rational Mech. Anal.,88, 223–270 (1985).
Ladyzhenskaya O. A., andUral'tseva N. N., Linear and Quasilinear Equations of Elliptic Type [in Russian], Nauka, Moscow (1973).
Ball, J. M., “A version of the fundamental theorem for Young measures,” in: Partial Differential Equations and Continuum Models of Phase Trans, Springer-Verlag, Berlin, Heidelberg, and New York, 1989, pp. 241–259. (Lecture Notes in Physics,344).
Murat F., “Compacite par compensation,” Ann. Scuola Norm. Sup. Pisa Cl. Sci. Fis. Math.,5, 89–507 (1978).
Additional information
The research was supported by the Russian Foundation for Basic Research (Grant 97-01-00459) and the International Science Foundation (Grant NMB000).
Leipzig, Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 41, No. 2, pp. 400–420, March–April, 2000.
Rights and permissions
About this article
Cite this article
Luckhaus, S., Plotnikov, P.I. Entropy solutions to the Buckley-Leverett equations. Sib Math J 41, 329–348 (2000). https://doi.org/10.1007/BF02674603
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02674603