The problem of start control for a class of semilinear distributed systems of Sobolev type

A result on the solvability of the Cauchy problem for a semilinear equation of Sobolev type in a Banach space is obtained with the help of the theory of degenerate operator semigroups. The result is used for investigating the problem of start control in the corresponding system. Abstract results are illustrated by the example of the semilinear Dzektser equation.