ABSTRACT
A multiplicative partial differential equation (MPDE) describes a relation between an unknown function and its multiplicative partial derivatives. The analysis of MPDEs has many facets. The classical approach is to develop methods for finding explicit solutions. The aim is to discover some of the solution properties before computing it, and sometimes even without a complete solution. There exist many equations that cannot be solved. All the authors can do in these cases is to obtain qualitative information on the solution. Furthermore, it is desired in many cases that the solution will be unique, and that it will be stable under small perturbations of the data. A theoretical understanding of the equation enables us to check whether these conditions are satisfied.
