Literature cited
N. V. Zhitarashu, “Theorems on the isomorphisms in the L2-theory of the weak solutions of parabolic boundary-value problems,” Dokl. Akad. Nauk SSSR,260, No. 5, 1054–1058 (1981).
S. D. Ivasishen, “The adjoint Green operators. Generalized solutions of parabolic problems with normal boundary conditions,” Dokl. Akad. Nauk SSSR,197, No. 2, 261–264 (1971).
J.-L. Lions and E. Magenes, Nonhomogeneous Boundary-Value Problems and Their Applications [Russian translation], Mir, Moscow (1971).
G. S. Gupalo, “On the Dirichlet problem for the Poisson equation,” [in Ukrainian], Visn. Lvov. Univ., Ser. Mekh.-Mat., No. 11, 21–25 (1976).
A. S. Gupalo and G. P. Lopushanskaya, “On a representation of the solution of the generalized boundary-value problem for a Petrovskii-elliptic system of differential equations,” Ukr. Mat. Zh.,37, No. 1, 128–131 (1985).
Ya. A. Roitberg and Z. G. Sheftel', “A theorem on homeomorphisms for elliptic systems and its applications,” Mat. Sb.,78, No. 3, 446–472 (1969).
S. D. Ivasishen, “The Green matrix of a nonhomogeneous parabolic boundary-value problem,” Dokl. Akad. Nauk SSSR,187, No. 4, 730–733 (1969).
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Am. Math. Soc. (1967).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 38, No. 6, pp. 795–798, November–December, 1986.
Rights and permissions
About this article
Cite this article
Lopushanskaya, G.P. Solution of the parabolic boundary-value problem in a space of generalized functions with the help of the green matrix. Ukr Math J 38, 674–677 (1986). https://doi.org/10.1007/BF01056659
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01056659