2019
Том 71
№ 11

# Cauchy problem for an essentially infinite-dimensional parabolic equation with variable coefficients

Bogdanskii Yu. V.

Abstract

The Cauchy problem for the equation $\cfrac{\partial u}{\partial t} = \mathcal{L}_x u = j(x) (u_x'')$ with positive essentially infinite-dimensional functionals $j(x)$ is studied in a certain Banach space of functions on an infinite-dimensional separable real Hilbert space.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 6, pp 714-724.

Citation Example: Bogdanskii Yu. V. Cauchy problem for an essentially infinite-dimensional parabolic equation with variable coefficients // Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 663–670.

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