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- W2561013173 abstract "This paper investigates the existence of a uniform in time $L^{∞}$ bounded weak entropy solution for the quasilinear parabolic-parabolic Keller-Segel model with the supercritical diffusion exponent $0<m<2-frac{2}{d}$ in the multi-dimensional space ${mathbb{R}}^d$ under the condition that the $L^{frac{d(2-m)}{2}}$ norm of initial data is smaller than a universal constant. Moreover, the weak entropy solution $u(x,t)$ satisfies mass conservation when $m>1-frac{2}{d}$ . We also prove the local existence of weak entropy solutions and a blow-up criterion for general $L^1cap L^{∞}$ initial data." @default.
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- W2561013173 date "2017-01-01" @default.
- W2561013173 modified "2023-09-30" @default.
- W2561013173 title "Uniform $L^{∞}$ boundedness for a degenerate parabolic-parabolic Keller-Segel model" @default.
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- W2561013173 doi "https://doi.org/10.3934/dcdsb.2017015" @default.
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