Literature Cited
N. A. Lar'kin, V. A. Novikov, and N. N. Yanenko, Nonlinear Equations of Variable Type [in Russian], Nauka, Novosibirsk (1983).
S. A. Tersenov, Introduction to the Theory of Equations of Parabolic Type with Varying Direction of Time [in Russian], Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR (1982).
N. N. Yanenko, “Nonlinear equations of varible type,” J. Sov. Math.,21, No. 5 (1983).
V. A. Rudyak, N. N. Yanenko, “The influence of effects of nonlocality and memory on processes of transfer,” Numerical Methods of Mechanics of a Solid Medium, Vol. 11, No. 3, ITPM SO AN SSSR, Novosibirsk (1980), pp. 132–140.
N. N. Yanenko, “Equations with coefficient of viscosity of variable sign,” Computational Methods in Mathematical Physics, Geophysics and Optimal Control, Nauka, Novosibirsk (1978), pp. 29–33.
E. N.Gokhman, Yu. K. Tovbin, and V. K. Fedyanin, “Concentration dependence of surfaces and solid diffusion in regular structures,” Physics of Interphase Phenomena, Nal'chik (1981), pp. 145–153.
N. N. Yanenko and V. A. Novikov, “A certain model of liquid with coefficient of viscosity with varying sign,” Numerical Methods of Mechanics of a Solid Medium, Vol. 4, No. 2, ITPM SO AN SSSR (1973), pp. 142–147.
T. I. Zelenyak, V. A. Novikov, and N. N. Yanenko, “Properties of solutions of nonlinear equations of variable type,” Numerical Methods of Mechanics of a Solid Medium, Vol. 5, No. 4, ITPM SO AN SSSR (1974), pp. 35–47.
V. S. Belonosov and T. I. Zelenyak, Nonlocal Problems in the Theory of Quasilinear Parabolic Equations [in Russian], Novosibirsk State Univ. (1975).
M. M. Lavrent'ev, Jr., “Properties of approximate solutions of nonlinear equations of variable type,” Sib. Mat. Zh.,21, No. 6, 176–185 (1980).
N. I. Maslova and V. A. Novikov, Numerical Investigation of an Equation with Coefficient of Varying Sign Multiplying the Second Derivative [in Russian], Preprint, AN SSSR, Sib. Otd., ITPM, No. 17, Novosibirsk (1980).
V. F. Kim and G. I. Zelinskaya, “Numerical solution of certain equations with coefficient of viscosity of variable sign,” Numerical Methods of Mechanics of a Solid Medium, Vol. 12, No. 1, ITPM SO AN SSSR, Novosibirsk (1981), pp. 54–68.
V. N. Grebenev and V. A. Novikov, “Properties of solutions of a stationary equation of variable type,” Numerical Methods of Mechanics of a Solid Medium, Vol. 11, No. 5, ITPM SO AN SSSR, Novosibirsk (1980), pp. 45–53.
K. Höllig, “Existence of infinitely many solutions for a forward backward heat equation,” Trans. Am. Math. Soc.,278, No. 1, 299–316 (1983).
V. A. Novikov, “Theorems of existence and nonexistence for a certain class of equations of variable type,” Dokl. Akad. Nauk SSSR,253, No. 6, 1311–1313 (1980).
A. G. Podgaev, “Some well-posed problems for equations of variable type,” Din. Sploshnoi Sredy, No. 55, 143–153 (1982).
A. S. Kalashnikov, “A Cauchy problem for second-order degenerate parabolic equations with power nonlinearities,” Proceedings of the I. G. Petrovskii Seminar, No. 6, Moscow State Univ. (1981), pp. 83–96.
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).
V. S. Belonosov, “Estimates of solutions of parabolic systems in weighted Hölder classes and some of their applications,” Mat. Sb.,110(152), No. 2, 163–188 (1979).
M. M. Lavrent'ev, Jr., “A priori estimates of solutions of nonlinear parabolic equations,” Differents. Uravn.,18, No. 5, 868–877 (1982).
M. M. Lavrent'ev, Jr., “A priori estimates of solutions of parabolic equations in regions with noncylindrical boundaries,” Din. Sploshnoi Sredy, No. 58, 94–107 (1982).
Additional information
Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 28, No. 2, pp. 79–95, March–April, 1987.
Rights and permissions
About this article
Cite this article
Lavrent'ev, M.M. Solvability of boundary-value problems for certain parabolic equations with degeneracies. Sib Math J 28, 239–253 (1987). https://doi.org/10.1007/BF00970870
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970870