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# $L^\infty$-decay property for quasilinear degenerate parabolic-elliptic Keller-Segel systems

• This paper deals with quasilinear degenerate Keller-Segel systems of parabolic-elliptic type. In this type, Sugiyama-Kunii [10] established the $L^r$-decay ($1\leq r<\infty$) of solutions with small initial data when $q\geq m+\frac{2}{N}$ ($m$ denotes the intensity of diffusion and $q$ denotes the nonlinearity). However, the $L^\infty$-decay property was not obtained yet. This paper gives the $L^\infty$-decay property in the super-critical case with small initial data.
Mathematics Subject Classification: Primary: 35K57; Secondary: 35B33.

 Citation:

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