arXiv Open Access 2024

A quasilinear Keller-Segel model with saturated discontinuous advection

Maria Gualdani Mikel Ispizua Nicola Zamponi

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Abstrak

We consider the singular limit of a chemotaxis model of bacterial collective motion recently introduced in arXiv:2009.11048 [math.AP]. The equation models aggregation-diffusion phenomena with advection that is discontinuous and depends sharply on the gradient of the density itself. The quasi-linearity of the problem poses major challenges in the construction of the solution and complications arise in the proof of regularity. Our method overcomes these obstacle by relying solely on entropy inequalities and the theory of monotone operators. We provide existence, uniqueness and smoothing estimates in any dimensional space.

Topik & Kata Kunci

math.AP math-ph

Penulis (3)

Maria Gualdani

Mikel Ispizua

Nicola Zamponi

Format Sitasi

APA MLA BibTeX

Gualdani, M., Ispizua, M., Zamponi, N. (2024). A quasilinear Keller-Segel model with saturated discontinuous advection. https://arxiv.org/abs/2403.06820

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓