Global solvability of some semilinear equations of Sobolev type

In the work existence of unique strong solution on the given segment of the Cauchy and Showalter problems for two classes of semilinear differential first order equations in Banach spaces unsolved with respect to the derivative is shown with using of methods of degenerate operator semigroups theory. Abstract results are illustrated on the example of semilinear Dzektser equation.