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

• Date: 1994
• Main Authors: Bogdanskii, Yu. V., Богданский, Ю. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1994
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5693
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.