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Limit passage in quasilinear parabolic equations with weakly converging coefficients, and the asymptotic behavior of solutions of the Cauchy problem. (English. Russian original) Zbl 0743.35009
Math. USSR, Sb. 70, No. 2, 467-484 (1991); translation from Mat. Sb. 181, No. 8, 1031-1047 (1990).
The author studies the asymptotic behavior (for \(t\to+\infty\) and every \(x\in\mathbb{R}^ n)\) of the solutions of the Cauchy problems for quasilinear parabolic equations with weakly convergent coefficients. These results extend some due to V. V. Zhikov [ibid. 33, 519-537 (1977; Zbl 0398.35048); ibid. 38, 279-292 (1981; Zbl 0462.35006); Trans. Mosc. Math. Soc. 1984, No. 2, 69-99 (1984; Zbl 0576.35049)] and those due to A. G. Sorokina [Math. Notes 34, 541-546 (1984; Zbl 0557.35063)]. An example is also presented.
35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
35K15 Initial value problems for second-order parabolic equations
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