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

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.