In this paper I discuss a generalization of the well-known Kardar–Parisi–Zhang (KPZ) equation that includes long-range interactions. This Non-local Kardar–Parisi–Zhang (NKPZ) equation has been suggested in the past to describe physical phenomena such as burning paper or deposition of...

In this paper, I analyze a generalization of the molecular-beam-epitaxy equation (with spatially correlated noise) that takes into account long-range interactions of a volume conserving surface. This equation is, therefore, called the non-local molecular-beam-epitaxy (NMBE) equation, sometimes...

In this paper we discuss nonlocal growth equations such as the generalization of the Kardar–Parisi–Zhang (KPZ) equation that includes long-range interactions, also known as the Nonlocal-Kardar–Parisi–Zhang (NKPZ) equation, and the nonlocal version of the molecular-beam-epitaxy (NMBE)...