  We investigate the process of an inhomogeneous planetesimal disk evolution
caused by the planetesimal-planetesimal gravitational scattering. We develop a
rather general approach based on the kinetic theory which self-consistently
describes the evolution in time and space of both the disk surface density and
its kinematic properties -- dispersions of eccentricity and inclination. The
gravitational scattering of planetesimals is assumed to be in the
dispersion-dominated regime which considerably simplifies analytical treatment.
The resultant equations are of advection-diffusion type. Distance dependent
scattering coefficients entering these equations are calculated analytically
under the assumption of two-body scattering in the leading order in Coulomb
logarithm. They are essentially nonlocal in nature. Our approach allows one to
explore the dynamics of nonuniform planetesimal disks with arbitrary mass and
random velocity distributions. It can also naturally include other physical
mechanisms which are important for the evolution of such disks -- gas drag,
migration, and so on.
