The structure of the category of parabolic equations

Details The structure of the category of parabolic equations The structure of the category of parabolic equations

2005-12-05

arxiv.org/abs/math/0512094v5

Mathematics

Analysis of PDEs

33 pages. Text improved and extended

Scientific paper

We define here the category of partial differential equations. Special cases of morphisms from an object (equation) are symmetries of the equation and reductions of the equation by a symmetry groups, but there are many other morphisms. We are mostly interested in a subcategory that arises from second order parabolic equations on arbitrary manifolds. We introduce a certain structure in this category enabling us to find the simplest representative of every quotient object of the given object, and develop a special-purpose language for description and study of structures of this kind. An example that deals with nonlinear reaction-diffusion equation is discussed in more detail.

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