Heat equation solutions on hyperbolic space H^d converge at sharp rates to non-universal asymptotic profiles that remember the initial mass distribution, obtained by treating time-dependent entropy minimizers as profiles.
On convex sobolev inequalities and the rate of convergence to equilibrium for fokker-planck type equa- tions.Communications in Partial Differential Equations, 26(1–2):43–100, 2001
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Sharp asymptotic behaviour of symmetric and non-symmetric solutions of the Heat Equation in the Hyperbolic Space
Heat equation solutions on hyperbolic space H^d converge at sharp rates to non-universal asymptotic profiles that remember the initial mass distribution, obtained by treating time-dependent entropy minimizers as profiles.