On a solution of the Cauchy problem in the weighted spaces of Beurling ultradistributions

Abstract

Results of Da Prato and Sinestrari \cite {d81} 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 $\mathbb R^d$. For this purpose, the new structural theorems were given for $\DD '^{(s)}_{L^p}((0,T)\times U)$. Then a class of the Cauchy problems in the general setting of such spaces of ultradistributions is analyzed.