A Nonlinear Nonlocal Multi-dimensional Conservation Law

We study a continuous model which describes the mass transport in droplet dispersions. The model is formulated as a conservation law with several spacevariables, ­n ­ Gn. m ­ Hjn. q q s0, ­ t ­ r js1 ­ xj for t)0, r)0, xj)0, and mjs1 xjs1, where G,Hj js1, . . . , m.are nonlocal functions of the unknown n t, r, x1, . . . , xm.; moreover, they have exponential singularities at rs0. We prove global existence and uniqueness and establish some numerical properties of the solution