The Condition of Generating Analytic Semigroup of an Operator Matrix and Existence of Solutions for an Abstract Quasilinear Differential Equations of Order 2 in Banach Spaces

摘要

In this paper were studied a sufficient condition for an operator matrix to generate an analytic semigroup in the product of Banach spaces, the domain of which is restricted by some supplementary conditions, and on the basis of it, an operational differential equations of order 2. The condition of generating analytic semigroup is obtained using the properties of projection operators in Banach space and purturbation theory of operators.