Literature cited
V. I. Averbukh, O. G. Smolyanov, and S. V. Fomin, “Generalized functions and differential equations in linear spaces. II,” Trans. Moscow Math. Soc.,27, 255–270 (1972).
Yu. V. Bogdanskii, “A maximum principle for nonregular elliptic differential equation in a Hilbert space of countable dimension,” Ukr. Math. J.,40, No. 1, 17–20 (1988).
A. Robertson and W. Robertson, Topological Vector Spaces, Cambridge University Press (1964).
Yu. L. Daletskii, “Infinite-dimensional elliptic operators and parabolic equations connected with them,” Russian Math. Surveys,22, No. 4, 3–54 (1967).
G. E. Shilov, “On some questions of analysis in a Hilbert space. III,” Math. USSR-Sb.,3, No. 1, 153–158 (1967).
E. M. Polishchuk, “On functional analogs of the heat-transfer equation,” Sib. Mat. Zh.,6, No. 6, 1322–1331 (1965).
I. Ya. Dorfman, “On the heat-transfer equation on a Hilbert space,” Vestn. Mosk. Univ., No. 4, 46–51 (1971).
Yu. V. Bogdanskii, “The Cauchy problem for parabolic equations with essentially infinitedimensional elliptic operators,” Ukr. Math. J.,29, No. 6, 578–581 (1978).
Yu. V. Bogdanskii, “Parabolic equations with essentially infinite-dimensional elliptic operators,” Deposited at UkrNIINTI, No. 4B269-77, Kiev (1977).
Yu. L. Daletskii and S. V. Fomin, Measures and Differential Equations in Infinite-Dimensional Spaces [in Russian], Nauka, Moscow (1983).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 5, pp. 584–590, May, 1989.
Rights and permissions
About this article
Cite this article
Bagdanskii, Y.V. Cauchy problem for heat-transfer equation with irregular elliptic operator. Ukr Math J 41, 506–510 (1989). https://doi.org/10.1007/BF01060533
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01060533