Exponential convergence for ultrafast diffusion equations with log‐concave weights
Abstract
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 Iacobelli [Discrete Contin. Dyn. Syst. 39 (2019), 4929–4943]. This equation is motivated by the gradient flow approach to the problem of quantization of measures introduced in Caglioti, Golse, and Iacobelli [Math. Models Methods Appl. Sci. 25 (2015), 1845–1885].
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Differential Equations and Numerical Methods
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 9
- Publication date
- 1 September 2026
- Language
- EN