  Results of Da Prato and Sinestrari, on differential operators with non-dense
domain but satisfying the Hille--Yosida condition, are applied in the setting
of Beurling weighted spaces of ultradistributions
  $\DD'^{(s)}_{L^p}((0,T)\times U)$, where $U$ is open and bounded set in
$\mathbb R^d$.
