In this paper, we study the global existence of positive solutions to the norm-preserving non-local heat flow of the porous-media type equations partial derivative(t)u = Delta u(r) + lambda(t)u(p), M x (0, infinity) on the compact Riemannian manifold (M, g) with the Cauchy data u(0) > 0 on M, where r >= 1, p > 1 and lambda(t) is chosen to make the L-2-norm of the solution u (or a power of u) constant. We show that the limit is an eigenfunction for the Laplacian operator. We use some tricky estimates through t...
