Exponential convergence for ultrafast diffusion in R^n with Gaussian weights is proved by a direct Poincaré inequality, extending prior one-dimensional results.
Exponential convergence for ultrafast diffusion equations with log-concave weights
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abstract
We study the asymptotic behavior of a weighted ultrafast diffusion PDE on the real line, with a log-concave and log-lipschitz weight, and prove exponential convergence to equilibrium. This result goes beyond the compact setting studied in [22]. This equation is motivated by the gradient flow approach to the problem of quantization of measures introduced in [11].
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On the exponential convergence to equilibrium for ultrafast diffusion equations
Exponential convergence for ultrafast diffusion in R^n with Gaussian weights is proved by a direct Poincaré inequality, extending prior one-dimensional results.