
In this paper, we study the existence and asymptotic behavior to a diffusion system which is non-local in time. As consequence of our theorems we deduce new results for the fractional-in-time Keller-Segel model. Our approach is intimately related with the Sonine kernels.
chemotaxis aggregation, Quasilinear parabolic equations, Sonine kernels, Asymptotic behavior of solutions to PDEs, diffusion, existence, Fractional partial differential equations, Keller-Segel model, Initial value problems for second-order parabolic systems, Cell movement (chemotaxis, etc.), asymptotic behavior, Integral equations with miscellaneous special kernels, Integro-differential operators
chemotaxis aggregation, Quasilinear parabolic equations, Sonine kernels, Asymptotic behavior of solutions to PDEs, diffusion, existence, Fractional partial differential equations, Keller-Segel model, Initial value problems for second-order parabolic systems, Cell movement (chemotaxis, etc.), asymptotic behavior, Integral equations with miscellaneous special kernels, Integro-differential operators
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