Cauchy problem for the essentially infinite-dimensional heat equation on a surface in a Hilbert space

It is proved that the Cauchy problem for a simple parabolic equation with essentially infinite-dimensional coefficients on bounded level surfaces of smooth functions in a Hilbert space is uniformly well posed.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 737–746, June, 1995.This work was supported by the Ukrainian State Committee on Science and Technology and (partially) by the International Science Foundation, Grant No. U44000.