journal article Jul 01, 1994

On a certain system of degenerate parabolic equations which arises in hydrodynamics

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References
19
[1]
G. I. Barenblatt, N. L. Galerkina, and M. V. Duneva, “Evolution of a burst of turbulence,” Inzh.-Fiz. Zh.,53, No. 5, 733–740 (1987).
[2]
A. S. Kalashnikov, “On some nonlinear systems that describe the dynamics of competing biological species,” Mat. Sb.,133, No. 1, 11–24 (1987).
[3]
A. S. Kalashnikov, “A class of systems of ‘reaction-diffusion’ type,” Trudy Sem. Petrovsk., No. 14, 78–88 (1983).
[4]
S. Takasi, “On the support properties of solutions for some degenerate quasilinear parabolic systems,” Nonlinear Anal.,14, No. 9, 789–805 (1990). 10.1016/0362-546x(90)90107-r
[5]
M. Bertsch and S. Kamin, “A system of degenerate parabolic equations,” SIAM J. Math. Anal.,21, No. 4, 905–916 (1990). 10.1137/0521050
[6]
A. S. Kalashnikov, “Diffusion of mixtures in the presence of long-long action,” Zh. Vychisl. Mat. i Mat. Fiziki,31, No. 3, 424–435 (1991).
[7]
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).
[8]
A. Friedman, Partial Differential Equations of Parabolic Type [Russian translation], Mir, Moscow (1968).
[9]
E. Di Benedetto and A. Friedman, “Hölder estimates for nonlinear degenerate parabolic systems,” J. Reine Angew. Math.,357, 1–22 (1985).
[10]
A. S. Kalashnikov, “Questions of the theory of degenerate parabolic equations,” Uspekhi Mat. Nauk,42, No. 2, 135–174 (1987).
[11]
S. N. Antontsev, Localization of Solutions to Degenerate Equations of Continuum Mechanics [in Russian], Inst. Gidrodinamiki (Novosibirsk), Novosibirsk (1986).
[12]
B. F. Knerr, “The behavior of the support of solutions of the equation of nonlinear heat conduction with absorption in one dimension,” Trans. Amer. Math. Soc.,249, No. 2, 409–424 (1979). 10.1090/s0002-9947-1979-0525681-7
[13]
J. L. Vázquez, “Asymptotic behaviour and propagation properties of the one-dimensional flow of a gas in a porous medium,” Trans. Amer. Math. Soc.,277, No. 2, 507–527 (1983). 10.1090/s0002-9947-1983-0694373-7
[14]
D. Aronson, M. G. Crandall, and L. A. Peletier, “Stabilisation of solutions of a degenerate nonlinear diffusion problem,” Nonlinear Anal., TMA,6, No. 10, 1001–1002 (1982). 10.1016/0362-546x(82)90072-4
[15]
A. S. Kalashnikov, “On differential properties of generalized solutions to equations of nonstationary filtration,” Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 1, 62–67 (1974).
[16]
M. A. Herrero and J. L. Vázquez, “The one-dimensional nonlinear heat equation with absorption: regularity of solutions and interfaces,” SIAM J. Math. Anal.,18, No. 1, 149–167 (1987). 10.1137/0518011
[17]
A. S. Kalashnikov, “Formation of singularities in solutions to the equation of nonstationary filtration,” Zhurn. Vychisl. Mat. i Mat. Fiziki,7, No. 2, 440–444 (1967).
[18]
B. F. Knerr, “The porous medium equation in one dimension,” Trans. Amer. Math. Soc.,234, No. 2, 381–415 (1977). 10.1090/s0002-9947-1977-0492856-3
[19]
V. S. Maderich, V. I. Nikishov, and A. G. Stetsenko, Dynamics of Interior Mixture in a Stratified Medium [in Russian], Naukova dumka, Kiev (1988).
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Published
Jul 01, 1994
Vol/Issue
35(4)
Pages
670-682
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V. N. Grebenev (1994). On a certain system of degenerate parabolic equations which arises in hydrodynamics. Siberian Mathematical Journal, 35(4), 670-682. https://doi.org/10.1007/bf02106610