Bifurcations of Spatially Inhomogeneous Solutions in Two Versions of the Nonlocal Erosion Equation

A periodic boundary-value problem for two versions of the nonlocal erosion equation is considered. This equation belongs to the class of partial differential equations with deviating spatial arguments. The issue of bifurcations of spatially inhomogeneous solutions is studied for the periodic boundary-value problem. In order to study the problem, we use the method of integral manifolds and normal forms.