Displaying similar documents to “Explicit exponential decay bounds in quasilinear parabolic problems.”

Boundedness in a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source

Ji Liu, Jia-Shan Zheng (2015)

Czechoslovak Mathematical Journal

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We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of...

On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis

Piotr Biler, Lorenzo Brandolese (2009)

Studia Mathematica

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We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.