Global Existence of Solutions to a Parabolic-Elliptic System of Drift-Diffusion Type in R2

Toshitaka Nagai; Takayoshi Ogawa

doi:10.1619/fesi.59.67

Global Existence of Solutions to a Parabolic-Elliptic System of Drift-Diffusion Type in R²

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Keywords: Interaction particle, Gravitational model, Chemotaxis model, Global existence, Subcritical case, Two dimensions

JOURNAL FREE ACCESS

2016 Volume 59 Issue 1 Pages 67-112

DOI https://doi.org/10.1619/fesi.59.67

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Abstract

We consider the Cauchy problem of a parabolic-elliptic system in R², which appears in various fields in physics and biology. Under a mild restriction on the initial data, we show the global existence of nonnegative solutions to the Cauchy problem for both the subcritical and the critical cases, that is, the total mass of the solution is less than or equal to 8π.

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