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Siberian Mathematical Journal

, Volume 33, Issue 6, pp 987–998 | Cite as

On asymptotic behavior of a solution to the cauchy problem for quasilinear parabolic equations

  • V. L. Kamynin
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Keywords

Asymptotic Behavior Cauchy Problem Parabolic Equation Quasilinear Parabolic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S. N. Kruzhkov and V. L. Kamynin, “The convergence of solutions to quasilinear parabolic equations with weakly convergent coefficients,” Dokl. Akad. Nauk SSSR,270, No. 3, 533–536 (1983).Google Scholar
  2. 2.
    S. N. Kruzhkov and V. L. Kamynin, “On passage to a limit in quasilinear parabolic equations,” Trudy Mat. Inst. Steklov.,167, 183–206 (1985).Google Scholar
  3. 3.
    V. L. Kamynin, “On passage to a limit in quasilinear elliptic equations with several independent variables,” Mat. Sb.,132, No. 1, 45–63 (1987).Google Scholar
  4. 4.
    V. L. Kamynin, “On continuous dependence of solutions to parabolic equations upon variations of coefficients in weak norms,” in: Analysis of Mathematical Models for Physical Processes [in Russian], Energoatomizdat, Moscow, 1988, pp. 41–48.Google Scholar
  5. 5.
    V. L. Kamynin, “Passage to a limit in quasilinear parabolic equations with weakly convergent coefficients and asymptotic behavior of solutions to the Cauchy problem,” Mat. Sb.,181, No. 8, 1031–1047 (1990).Google Scholar
  6. 6.
    S. N. Kruzhkov, “Nonlinear parabolic equations with two independent variables,” Trudy Moskov. Mat. Obshch.,16, 329–346 (1967).Google Scholar
  7. 7.
    N. V. Krylov and M. V. Safonov, “A certain property of solutions to parabolic equations with measurable coefficients,” Izv. Akad. Nauk SSSR Ser. Mat.,44, No. 1, 161–175 (1980).Google Scholar
  8. 8.
    V. L. Kamynin, “Asymptotic behavior of solutions to the Cauchy problem for nondivergence parabolic equations,” Dokl. Akad. Nauk SSSR,316, No. 4, 807–811 (1991).Google Scholar
  9. 9.
    V. D. Repnikov and S. D. Eįdel'man, “Necessary and sufficient conditions for stabilization of a solution to the Cauchy problem,” Dokl. Akad. Nauk SSSR,167, No. 2, 298–301 (1966).Google Scholar
  10. 10.
    A. K. Gushchin and V. P. Mikhaįlov, “On stabilization of a solution to the Cauchy problem for a parabolic equation with a single space variable,” Trudy Mat. Inst. Steklov.,112, 181–202 (1971).Google Scholar
  11. 11.
    F. O. Porper and S. D. Eįdel'man, “Asymptotic behavior of classical and generalized solutions to one-dimensional parabolic equations of the second order,” Trudy Moskov. Mat. Obshch.,36, 85–130 (1978).Google Scholar
  12. 12.
    V. V. Zhikov and M. M. Sirazhudinov, “Averaging nondivergence second order elliptic and parabolic operators and stabilization of a solution to the Cauchy problem,” Mat. Sb.,116, No. 2, 166–186 (1981).Google Scholar
  13. 13.
    V. V. Zhikov, “On stabilization of solutions to parabolic equations,” Mat. Sb.,104, No. 4, 597–616 (1977).Google Scholar
  14. 14.
    A. Friedman, Partial Differential Equations of Parabolic Type [Russian translation], Mir, Moscow (1968).Google Scholar
  15. 15.
    O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).Google Scholar
  16. 16.
    Yu. A. Altukhov and I. T. Mamedov, “The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients,” Mat. Sb.,131, No. 4, 477–500 (1986).Google Scholar
  17. 17.
    N. V. Krylov, Nonlinear Second Order Elliptic and Parabolic Equations [in Russian], Nauka, Moscow (1985).Google Scholar
  18. 18.
    N. V. Krylov, “On equations of minimax type in the theory of elliptic and parabolic equations in the plane,” Mat. Sb.,81, No. 1, 3–22 (1970).Google Scholar
  19. 19.
    V. V. Zhikov, “Pointwise stabilization criterion for the second order equations with almost periodic coefficients,” Mat. Sb.,110, No. 2, 304–318 (1979).Google Scholar
  20. 20.
    K. V. Valikov, “Closeness of solutions to the Cauchy problem for some parabolic equations of second order,” Differentsial'nye Uravneniya,23, No. 4, 686–696 (1987).Google Scholar
  21. 21.
    S. N. Kruzhkov, “Quasilinear parabolic equations and systems with two independent variables,” Trudy Sem. Petrovsk.,5, 217–272 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

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  • V. L. Kamynin

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