Asymptotic analysis for a very fast diffusion equation arising from the 1D quantization problem

Mikaela Iacobelli

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arXiv · 1602.08125

Asymptotic analysis for a very fast diffusion equation arising from the 1D quantization problem

Mikaela Iacobelli

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Abstract

In this paper we study the asymptotic behavior of a very fast diffusion PDE in 1D with periodic boundary conditions. This equation is motivated by the gradient flow approach to the problem of quantization of measures introduced in \cite{CGI1}. We prove exponential convergence to equilibrium under minimal assumptions on the data, and we also provide sufficient conditions for $W_2$-stability of solutions.

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BibTeX RIS

Mikaela Iacobelli. 2016-02-25. Asymptotic analysis for a very fast diffusion equation arising from the 1D quantization problem. https://arxiv.org/abs/1602.08125

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