Young integrals and SPDEs
نویسندگان
چکیده
In this note, we study the non-linear evolution problem dYt = −AYtdt +B(Yt)dXt, whereX is a γ-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 γ in (0, 1)), and then when B satisfies some Lipschitz type conditions (for γ > 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.
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