Young Integrals and SPDEs
Tóm tắt
In this note, we study the non-linear evolution problem
$$dY_t = -A Y_t dt + B(Y_t) dX_t,$$
where
$X$
is a
$\gamma$
-Hölder continuous function of the time parameter, with values in a distribution space, and
$-A$
the generator of an analytical semigroup. Then, we will give some sharp conditions on
$X$
in order to solve the above equation in a function space, first in the linear case (for any value of
$\gamma$
in
$(0,1)$
), and then when
$B$
satisfies some Lipschitz type conditions (for
$\gamma>1/2$
). The solution of the evolution problem will be understood in the mild sense, and the integrals involved in that definition will be of Young type.
Từ khóa
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