Work

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

Year: 2020

Type: preprint

Abstract: We consider the drift-diffusion equation $u_t-εΔu + \nabla \cdot(u\nabla K^*u)=0$ 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2009.12173

Authors: Biler, Piotr, Boritchev, Alexandre, Karch, Grzegorz, Laurençot, Philippe

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4298014246

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