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References
T. L. Zelenyak, “On qualitative properties of solutions to mixed quasilinear problems for equations of parabolic type,” Mat. Sb.,104, No. 3, 486–510 (1977).
M. P. Vishnevskiî, T. I. Zelenyak, and M. M. Lavrent’ev Jr., “Behavior of solutions to nonlinear parabolic equations at large time,” Sibirsk. Mat. Zh.,36, No. 3, 510–530 (1995).
T. I. Zelenyak, M. M. Lavrentiev, and M. P. Vishnevskii, Qualitative Theorie of Parabolic Equations, VSP, Tokyo and Utrecht (1997).
O. G. Provorova, “To the question of large time behavior of solutions to parabolic equations,” Differentsial’nye Uravneniya,5, No. 1, 108–114 (1969).
A. Kosha, Variational Calculus [Russian translation], Vysshaya Shkola, Moscow (1983).
M. H. Protter and H. F. Weinberger, “On the spectrum of general second order operators,” Bull. Amer. Math. Soc.,72, No. 2, 251–255 (1966).
T. I. Zelenyak, Qualitative Theory of Boundary Value Problems for Second-Order Quasilinear Equations of Parabolic Type [in Russian], Novosibirsk Univ., Novosibirsk (1972).
A. F. Filippov, “Conditions for existence of solutions to a quasilinear parabolic equation,” Dokl. Akad. Nauk SSSR,141, No. 3, 568–570 (1961).
S. N. Kruzhkov and O. A. Oleînik, “Second-order quasilinear parabolic equations in several independent variables,” Uspekhi Mat. Nauk,16, No. 5, 115–155 (1961).
S. N. Kruzhkov, “Quasilinear parabolic equations and systems in two independent variables,” Trudy Sem. Petrovsk., No. 5, 217–272 (1979).
O. A. Ladyzhenskaya and N. N. Ural’tseva, “A survey of results on the solvability of boundary value problems for quasilinear uniformly elliptic and parabolic equations of second order with unbounded singularities,” Uspekhi Mat. Nauk,41, No. 5, 59–83 (1986).
A. A. Samarskiî, V. A. Galaktionov, S. P. Kurdyumov, and A. P. Mikhaîlov, Blowups in Problems for Quasilinear Parabolic Equations [in Russian], Nauka, Moscow (1987).
S. B. Angenent and M. Fila, “Interior gradient blow-up in a semilinear parabolic equation,” Differential Integral Equations,9, No. 5, 865–877 (1996).
M. Fila and G. Lieberman, “Derivative blow-up and beyond for quasilinear parabolic equations,” Differential Integral Equations,7, No. 3–4, 811–821 (1994).
T. Dlotko, “Examples of parabolic problems with blowing-up derivatives,” J. Math. Anal. Appl.,154, No. 1, 226–237 (1991).
S. N. Bernshteîn, Collected Works. Vol. 3 [in Russian], Izdat. Akad. Nauk SSSR, Moscow (1960).
M. A. Sychëv, “To the question of regularity of solutions to variational problems,” Mat. Sb.,183, No. 4, 118–142 (1992).
J. M. Ball and V. J. Mizel, “Singular minimizers for regular one-dimensional problems in the calculus of variations,” Bull. Amer. Math. Soc. (N.S.),11, No. 1, 143–146 (1984).
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The research was financially suppoted by the “Russian Universities” program (Grant MM7.8 3H-303-92) and the Russian Foundation for Basic Research (Grant 96-01-01618).
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 39, No. 2, pp. 317–328, March–April, 1998.
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Zelenyak, T.I., Lyul’ko, N.A. To the question of global solvability of mixed problems for quasilinear parabolic equations. Sib Math J 39, 277–288 (1998). https://doi.org/10.1007/BF02677511
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DOI: https://doi.org/10.1007/BF02677511