Convergence of a heat flow on a Hilbert manifold

Source abstract

We study the heat flow projected on a manifold M ⊂ L 2 (Ω). This manifold is defined by the condition that the integrals ∫ Ω u k ( t,x ) d x , k = 1,…, N , are constants of motion. We show that solutions to this problem converge to a steady state as time tends to +∞. We use in an essential way a variant of the Łojasiewicz inequality.