NETWORKS AND HETEROGENEOUS MEDIA, v.14, no.3, pp.471 - 487
Abstract
We consider the 1D transport equation with nonlocal velocity field: theta(t) + u theta(x) + nu Lambda(gamma)theta = 0, u = N(theta), where N is a nonlocal operator and Lambda(gamma) is a Fourier multiplier defined by (Lambda gamma f) over cap(xi) =vertical bar xi vertical bar(gamma)(f) over cap(xi). In this paper, we show the existence of solutions of this model locally and globally in time for various types of nonlocal operators.