@article{Cao2026, 
author = {Yang Cao and Chengyuan Qu and Benhui Wang},
title = {Stochastic pseudo-parabolic equation with logarithmic nonlinearity},
year = {2026},
journal = {Communications in Analysis and Mechanics},
volume = {18},
number = {1},
pages = {245-272},
keywords = {stochastic pseudo-parabolic equation, logarithmic nonlinearity, global solution, Galerkin method, non-local},
url = {https://www.sciopen.com/article/10.3934/cam.2026010},
doi = {10.3934/cam.2026010},
abstract = {This manuscript was dedicated to exploring the existence and uniqueness of global solutions pertaining to a specific class of stochastic pseudo-parabolic equations. These equations have logarithmic nonlinearity and are driven by Brownian motion. By utilizing the Galerkin method, Prokhorov's theorem, and Skorohod's embedding theorem, we proved the existence of a global solution in the weak probabilistic sense. Subsequently, by leveraging the uniqueness of solutions and applying the Yamada-Watanabe theorem, the global existence and uniqueness of a probability strong solution were established. A notable finding, in contrast to the stochastic heat equation, was that as the pseudo-parabolic coefficient    μ increased, the growth condition imposed on the noise coefficient within the stochastic pseudo-parabolic equation could be significantly relaxed.}
}