Global solution of nonlinear stochastic heat equation with solutions in a Hilbert manifold

Abstract

The objective of this paper is to prove the existence of a global solution to a certain stochastic partial differential equation subject to the [Formula: see text]-norm being constrained. The corresponding evolution equation can be seen as the projection of the unconstrained problem onto the tangent space of the unit sphere [Formula: see text] in a Hilbert space [Formula: see text].