Event № 73
I will define the category of partial differential equations. The objects of this category are partial differential equations (PDE) or systems of such equations, and the morphisms are some special surjective maps from the space of independent and dependent variables of the source equation to the space of independent and dependent variables of the target equation. The definition of the morphisms is dictated by the desire to ensure that the pullback by a morphism of any solution of the target equation is a solution of the source equation. I will illustrate the general definition by some simple examples, namely, the morphisms from first order PDE (in particular, PDE describing holomorphic submanifolds of a complex manifold) and the morphisms from nonlinear heat equations.