Siberian Mathematical Journal

, Volume 34, Issue 6, pp 1110–1116 | Cite as

Solvability of nonlinear parabolic problems

  • M. M. Lavrent'evJr.


Parabolic Problem Nonlinear Parabolic Problem 
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  1. 1.
    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
  2. 2.
    N. V. Krylov, Nonlinear Elliptic and Parabolic Equations of Second Order [in Russian], Nauka, Moscow (1985).Google Scholar
  3. 3.
    S. P. Samarskiî, V. A. Galaktionov, S. P. Kurdyumov, and A. P. Mikhaîlov, Peaking Modes in Problems for Quasilinear Parabolic Equations [in Russian], Nauka, Moscow (1987).Google Scholar
  4. 4.
    T. I. Zelenyak, “On qualitative properties of solutions to quasilinear mixed problems for equations of parabolic type,” Mat. Sb.,104, No. 3, 486–510 (1977).Google Scholar
  5. 5.
    S. N. Kruzhkov, “Nonlinear parabolic equations in two independent variables,” Trudy Moskov. Mat. Obshch.,16, 329–346 (1967).Google Scholar
  6. 6.
    S. N. Kruzhkov, “The fundamental a priori estimate for solutions to quasilinear parabolic equations,” Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk,16, No. 3, 16–20 (1972).Google Scholar
  7. 7.
    S. N. Bernshteîn, “On equations of the calculus of variations,” in: S. N. Bernshteîn, Collected Akad. Nauk SSSR, Moscow, 1960, pp. 191–242.Google Scholar
  8. 8.
    M. Nagumo, “Über die gleichmässige Summierbarkeit und ihre Anwendung auf ein Variation-sproblema,” Japan J. Math.,6, 173–182 (1929).Google Scholar
  9. 9.
    L. Tonelli, Fondamenti di Calcolo Della Variazioni. Vol. 11, Zanichelli, Bologna (1923).Google Scholar
  10. 10.
    S. N. Kruzhkov, “Quasilinear parabolic equations and systems in two independent variables,” Trudy Sem. Petrovsk., No. 5, 217–272 (1979).Google Scholar
  11. 11.
    A. F. Filippov, “Conditions for existence of solutions to quasilinear parabolic equation,” Dokl. Akad. Nauk SSSR,141, 568–570 (1961).Google Scholar
  12. 12.
    V. S. Belonosov and T. I. Zelenyak, Nonlocal Problems in the Theory of Quasilinear Parabolic Equations [in Russian], Izdat. Novosibirsk Univ, Novosibirsk (1975).Google Scholar
  13. 13.
    V. L. Kamynin, “A priori estimates and solvability in the large for quasilinear parabolic equations,” Vestnik Moscow. Univ. Ser. I. Mat. Mekh., No. 1, 33–38 (1981).Google Scholar
  14. 14.
    L. S. Pontryagin, Ordinary Differential Equations [in Russian], Nauka, Moscow (1965).Google Scholar

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© Plenum Publishing Corporation 1993

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  • M. M. Lavrent'evJr.

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