ABOUT STABILITY OF STRONGLY CONTINUOUS SEMIGROUPS GENERATED BY SUM OF TWO OPERATORS
We study the stability of solutions of differential equation; which left side is represented as the sum of two commuting unbounded operators. One of which generates strongly continuous one-parametric semigroup (С0-semigroup) and another one generates analytic semigroup. We study the case of infinite-dimensional space and investigate the conditions on generators of semigroups, which are located at the left-hand side of the equation. The aim of the article is to provide a method of proving the strong stability of semigroups generated by the sum of two commuting unbounded operators in Hilbert space. The proof is based on the methods associated with Tomilov's theorem, formulas of Da Prato - Grisvard and Yosida approximations.