Literature cited
M. I. Vishik, “Solvability of boundary value problems for quasilinear parabolic equations,” Mat. Sb.,59, No. 101, 289–325 (1962).
J. L. Lions, Certain Methods for Solving Nonlinear Boundary Value Problems [Russian translation], Mir, Moscow (1972).
Yu. A. Dubinskii, “Quasilinear elliptic and parabolic equations of arbitrary order,” Usp. Mat. Nauk,23, No. 1, 45–90 (1968).
F. E. Browder, “Strongly nonlinear parabolic boundary value problems,” Am. J. Math.,86, No. 2, 339–357 (1964).
T. Donaldson, “Inhomogeneous Orlicz—Sobolev spaces and nonlinear parabolic initial value problems,” J. Diff. Eq.,16, No. 2, 201–256 (1974).
M. A. Krasnosel'skii and Ya. B. Rutitskii, Convex Functions and Orlicz Spaces [in Russian], Nauka, Moscow (1958).
Chan Dyk Van, “Nontriviality of the Sobolev-Orlicz space of infinite order in a bounded domain of an Euclidean space,”, Dokl. Akad. Nauk SSSR,250, No. 6, 1331–1334 (1980).
S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Nauka, Moscow (1977).
Yu. A. Dubinskii (Ju. A. Dubinskii), Sobolev Spaces of Infinite Order and Differential Equations, Reidel, Dordrecht-Boston-Lancaster-Tokyo (1986).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 48, No. 1, pp. 78–85, July, 1990.
Rights and permissions
About this article
Cite this article
Chyong, N.M., Chung, L.K. & Van Nin', K. Boundary value problem for nonlinear parabolic equations of infinite order in Sobolev-Orlicz spaces. Mathematical Notes of the Academy of Sciences of the USSR 48, 673–677 (1990). https://doi.org/10.1007/BF01164267
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01164267