Maltsev A. Evolutionary equations with essentially infinite-dimensional operators

It is a theoretical investigation in the infinitedimensional analysis field. The solutions of the Cauchy problem for the non-stationary parabolic equation with essentially infinite-dimensional operators are constructed in a certain Banach space of functions on an infinite-dimensional separable real Hilbert space. It is proved that the Cauchy problem for the simplest non-stationary parabolic equation with essentially infinite-dimensional operators is well-posed. Evolutionary families are found for the non-stationary equations involving the essentially infinite-dimensional operators perturbed by vector fields of certain class. It is solved the Cauchy problem for the non-stationary parabolic equation with essentially infinite-dimensional coefficients on bounded surfaces of finite codimension in a Hilbert space.