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Sharp Sobolev estimates for concentration of solutions to an aggregation-diffusion equation

Abstract : We consider the drift-diffusion equation u t − ε∆u + ∇ · (u ∇K * u) = 0 in the whole space with global-in-time solutions bounded in all Sobolev spaces; for simplicity, we restrict ourselves to the model case K(x) = −|x|. We quantify the mass concentration phenomenon, a genuinely nonlinear effect, for radially symmetric solutions of this equation for small diffusivity ε studied in our previous paper [3], obtaining optimal sharp upper and lower bounds for Sobolev norms.
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https://hal.archives-ouvertes.fr/hal-02948312
Contributor : Alexandre Boritchev <>
Submitted on : Thursday, September 24, 2020 - 3:31:02 PM
Last modification on : Monday, September 28, 2020 - 11:00:29 AM

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  • HAL Id : hal-02948312, version 1
  • ARXIV : 2009.12173

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Piotr Biler, Alexandre Boritchev, Grzegorz Karch, Philippe Laurençot. Sharp Sobolev estimates for concentration of solutions to an aggregation-diffusion equation. 2020. ⟨hal-02948312⟩

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