For weighted ultrafast diffusion equations on R with log-concave, log-Lipschitz weights, solutions starting close to equilibrium converge exponentially fast in relative L2.
Iacobelli, Asymptotic analysis for a very fast diffusion equation arising from the 1D quantization problem, Discrete Contin
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Exponential convergence for ultrafast diffusion equations with log-concave weights
For weighted ultrafast diffusion equations on R with log-concave, log-Lipschitz weights, solutions starting close to equilibrium converge exponentially fast in relative L2.