First-Order Partial Differential Equation with a Nonlocal Boundary Condition

Abstract

In this paper, the initial value problem for the first-order partial differential equation with the nonlocal boundary condition is studied. The positivity of the space operator A(x) generated by this problem in interpolation spaces is established. The structure interpolation spaces of this space operator is investigated. The positivity of this space operator in Holder spaces is established. In applications, the stability estimates for the first-order partial differential equation with the nonlocal boundary condition are obtained.