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We investigate equations of the form Dtu = Δu + ξ∇u for an unknown function u(t, x), t ∈ ℝ, x ∈ X, where Dtu = a0(u, t) + Σ k=1rak(t, u)∂tku, Δ is the Laplace-Beltrami operator on a Riemannian manifold X, and ξ is a smooth vector field on X. More exactly, we study morphisms from this equation within the category PDE of partial differential equations, which was introduced...
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