Возмущенные начально-краевые задачи сопряжения

The paper studies perturbed initial-boundary value problems of conjugation generated by a sesquilinear form. The principle of superposition allows us to represent the solution of the original problem as a sum of solutions of auxiliary problems containing inhomogeneity either in the equation or in one of the boundary conditions. The original initial-boundary value problems are reduced to Cauchy problems for first-order integro-differential and differential operator equations in a Hilbert space. Theorems on the existence and uniqueness of time-strong solutions of the Cauchy problems for two domains are proved.