First-Order Differential-Operator Equation with Variable Domains of Piecewise Smooth Operators

摘要

We prove the existence, uniqueness, and smoothness of weak solutions of a firstorder differential-operator equation with variable domains of nonself-adjoint piecewise smooth operators for which one has the corresponding majorant operators. We analyze the wellposedness and smoothness of weak solutions of three new mixed problems with piecewise smooth (in time) coefficients in the equations of finite and infinite order and in the boundary conditions.