Cross-diffusion and traveling waves in porous-media flux-saturated Keller–Segel models
2018 ◽
Vol 28
(11)
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pp. 2103-2129
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Keyword(s):
Blow Up
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This paper deals with the analysis of qualitative properties involved in the dynamics of Keller–Segel type systems in which the diffusion mechanisms of the cells are driven by porous-media flux-saturated phenomena. We study the regularization inside the support of a solution with jump discontinuity at the boundary of the support. We analyze the behavior of the size of the support and blow-up of the solution, and the possible convergence in finite time toward a Dirac mass in terms of the three constants of the system: the mass, the flux-saturated characteristic speed, and the chemoattractant sensitivity constant. These constants of motion also characterize the dynamics of regular and singular traveling waves.
2014 ◽
Vol 418
(2)
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pp. 713-733
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1993 ◽
Vol 123
(3)
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pp. 433-460
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2016 ◽
Vol 144
(11)
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pp. 4845-4859
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