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

Mikaela Iacobelli

doi:10.3934/dcds.2019201

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2019, Volume 39, Issue 9: 4929-4943. Doi: 10.3934/dcds.2019201

This issue Previous Article Next Article Kato's type theorems for the convergence of Euler-Voigt equations to Euler equations with Drichlet boundary conditions

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

Mikaela Iacobelli

ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland

Received: February 2016

Published online: September 2019

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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 [3]. 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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Mathematics Subject Classification: Primary: 35K15, 35K65; Secondary: 70F45.

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References

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