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Cross-diffusion and traveling waves in porous-media flux-saturated Keller-Segel models. (arXiv:1810.07606v1 [math.AP])

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 towards 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.查看全文

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