Literature cited
V. V. Zhikov, “The stabilization of solutions of parabolic equations,” Mat. Sb.,104, No. 4, 597–616 (1977).
J. Nash, “Continuity of solutions of parabolic and elliptic equations,” Am. J. Math.,80, No. 4, 931–954 (1958).
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc. (1968).
N. G. Meyers, “An LP-estimate for the gradient of solutions of second-order elliptic divergence equations,” Ann. Scuola Norm. Sup. Pisa,17, 189–206 (1963).
A. Bensoussan, L. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam (1978).
A. K. Gushchin and V. P. Mikhailov, “The stabilization of solutions of Cauchy's problem for a parabolic equation,” Diff. Uravn.,7, No. 12, 297–311 (1971).
V. V. Zhikov, “The pointwise stabilization criterion for second-order parabolic equations with almost-periodic coefficients,” Mat. Sb.,110, No. 2, 304–318 (1979).
F. O. Porper and S. D. Éidel'man, “The asymptotic behavior of classical and generalized solutions of one-dimensional second-order parabolic equations,” Tr. Mosk. Mat. O-va,36, 85–130 (1978).
F. O. Porper and S. D. Éidel'man, “Theorems on the asymptotic closeness of solutions of multidimensional second-order parabolic equations,” Usp. Mat. Nauk,35, No. 1, 211–212 (1980).
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Translated from Matematicheskie Zametki, Vol. 34, No. 1, pp. 113–121, July, 1983.
The author is grateful to V. V. Zhikov and K. V. Valikov for setting the problem and supervising the work.
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Sorokina, A.G. Closeness of solutions of Cauchy's problem for second-order parabolic equations. Mathematical Notes of the Academy of Sciences of the USSR 34, 541–546 (1983). https://doi.org/10.1007/BF01160869
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DOI: https://doi.org/10.1007/BF01160869