Flows through nonhomogeneous porous media in an isolated environment
Authors:
Jingxue Yin and Wenjie Gao
Journal:
Quart. Appl. Math. 55 (1997), 333-346
MSC:
Primary 76S05; Secondary 35K35
DOI:
https://doi.org/10.1090/qam/1447581
MathSciNet review:
MR1447581
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Abstract: The nonhomogeneous gas or fluid flowing through a nonhomogeneous porous medium is studied. An interesting phenomenon is discussed which shows that the state of the flow is not affected by the surrounding environment if some hypotheses are made on the porosity of the gas, the viscosity, and the permeability of the medium. Such a state is called an isolated environment. The conditions under which the state of the gas depends on the surrounding environment are also discussed.
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D. G. Aronson, L. A. Caffarelli, and S. Kamin, How an initially stationary interface begins to move in porous medium flow, Univ. of Minnesota Math. Report 81-113, 1–41 (1981)
L. A. Caffarelli and A. Friedman, Regularity of the free boundary of a gas flow in an n-dimensional porous medium, Indiana Univ. Math. J. 29, 361–389 (1980)
L. A. Caffarelli, J. L. Vazquez, and N. I. Wolanski, Lipschitz continuity of solutions and interfaces of the N-dimensional porous medium equation, Indiana Univ. Math. J. 36(2), 327–401 (1987)
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A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Inc., 1964
A. Friedman and S. Kamin, The asymptotic behavior of gas in an n-dimensional porous medium, Trans. Amer. Math. Soc. 262, 551–563 (1980)
B. H. Gilding, Properties of solutions of an equation in the theory of infiltration, Arch. Rational Mech. Anal. 65, no. 3, 203–225 (1977)
A. S. Kalashnikov, Some problems of the qualitative theory of nonlinear degenerate second-order parabolic equations, Russian Math. Surveys 42:2, 169–222 (1987)
L. K. Martinson and K. B. Paplov, The effect of magnetic plasticity in non-Newtonian fluids, Magnit. Gidrodinamika 3, 69–75 (1969)
P. Z. Mkrtychyan, Uniqueness of the solution to the second initial-boundary value problem for an equation of non-Newtonian polytropic filtration, (Russian) Zap. Nauchn. Sem. S.-Peterberg Otdel. Mat. Inst. Steklov (POMI) 200 (1992); Kraev Zadachi Mat. Fiz. Smezh Voprosy Teor. Funktsii 24, 110–117, 189
J. R. King, Multidimensional singular diffusion, J. Engrg. Math. 27, 357–387 (1993)
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© Copyright 1997
American Mathematical Society