Existence and uniqueness of global solutions to the stochastic heat equation with superlinear drift on an unbounded spatial domain
Michael Salins · Stochastics and Dynamics · 2021
We prove the existence and uniqueness of global solutions to the semilinear stochastic heat equation on an unbounded spatial domain with forcing terms that grow superlinearly and satisfy an Osgood condition [Formula: see text] along with additional restrictions. For example, consider the forcing [Formula: see text]. A new dynamic weighting procedure is introduced to control the solutions, which are unbounded in space.