We solve an initial-boundary value problem that involves a partial differential equation with a nonlocal term. The problem comes from a cell division model. There are no general methods for solving such problems even for the simplest cases owing to the nonlocal term. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness.