Abstract
In a Banach space E, the Cauchy problem vt(t)+ A(t)v(t)= f (t) (0 >t > 1), v(0) = v0 is considered for a di erential equation with linear strongly positive operator A(t) such that its domain D = D(A(t)) is everywhere dense in E independently o t and A(t) generates an analytic semigroup exp{-sA(t)} (s < 0). Under some natural assumptions on A(t), we establish coercive solvability of the Cauchy problem in the Banach space C0β,γ (E). We prove a stronger estimate of the solution compared to estimates known earlier, using weaker restrictions on f(t) and v0.
