The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principle (Q2904718)
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scientific article; zbMATH DE number 6070861
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principle |
scientific article; zbMATH DE number 6070861 |
Statements
23 August 2012
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diffusion-aggregation model
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finite speed of propagation
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radially stationary solutions
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compactly supported weak solutions
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nonlocal aggregation term
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degeneracy of the diffusion term
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The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principle (English)
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The qualitative and asymptotic behavior of radially stationary solutions for a class of diffusion-aggregation equations is investigated. A universal estimate for compactly supported weak solutions is established. The challenge in the analysis consists of the nonlocal aggregation term as well as the degeneracy of the diffusion term, which generates compactly supported solutions. The key tools of the investigation of the considered problem are maximum-principle type arguments as well as estimates on mass concentration of solutions.
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