Existence and uniqueness of global solutions to the stochastic heat equation with superlinear drift on an unbounded spatial domain
Files
Accepted manuscript
Date
2021-12-28
Authors
Salins, Michael
Version
Accepted manuscript
OA Version
Citation
M. Salins. "Existence and uniqueness of global solutions to the stochastic heat equation with superlinear drift on an unbounded spatial domain." Stochastics and Dynamics, https://doi.org/10.1142/s0219493722500149
Abstract
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 R
1/|f(u)|du = +∞ along with additional restrictions. For example, consider the forcing f(u) = u log(e
e + |u|) log(log(e
e + |u|)). A
new dynamic weighting procedure is introduced to control the solutions, which are unbounded in space.