Existence and Uniqueness of Solutions to Semilinear Nonlocal Parabolic Equations

The Banach contraction mapping theorem and the theory of analytic semigroups are used to prove the existence and uniqueness of solutions to nonlocal semilinear parabolic partial differential equations. The equations consist of a parabolic boundary value problem and a relation connecting the initial value to values or weighted averages of values of the solution at other times.