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| The Cahn-Hilliard/Allen-Cahn equation with a noise perturbation is a simplified
mean field model of stochastic microscopic dynamics associated
with adsorption and desorption-spin flip mechanisms in the
context of surface processes. For such an equation we consider a
multiplicative space-time white noise with diffusion coefficient
of sub-linear growth in dimension 1 up to 3. Using technics from semigroup theory and parabolic operators in the sense
of Petrovsk\u{\i\i}, we
prove the existence and uniqueness of the solution, as well as its path regularity. Our results are also
valid for the stochastic Cahn-Hilliard equation with unbounded
noise diffusion, for which previous results were established only
in the framework of a bounded diffusion
coefficient. The path regularity of the stochastic
solution depends on the dimension and on that of the initial condition. |
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