ALMOST PERIODICALLY DISTRIBUTED SOLUTIONS FOR DIFFUSION-EQUATIONS IN DUALS OF NUCLEAR SPACES

We discuss the problem of the existence of almost periodic in distribu tion solutions of nuclear space-valued diffusion equations with almost periodic coefficients. Under a dissipativity condition we prove that the translation of the unique mean square bounded solution is almost p eriodically distributed. Similar results hold in the affine case under mean square stability of the linear part of the equation if the nucle ar space is a component of a special compatible family.