On a two-species cross attraction system in higher dimensions

2021/11/11 by Eric A. Carlen, Carlen, Eric A., Süleyman Ulusoy +1
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Mathematical Biology Tumor Growth #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2111.06154

openalex publication_date 2021/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3. Under the hypothesis of integrable initial data with finite second moment and energy, we show local-in-time existence for any mass of free-energy solutions, namely weak solutions with some free energy estimates. We exhibit that the qualitative behavior of solutions is decided by a set of critical values: there is a critical value of a parameter pair in the system of equations for which there is a global-in-time energy solution and there exist blowing-up free-energy solutions under a criticality condition is violated for the parameter pair.

Citations

• On explosions of solutions to a system of partial differential equations modelling chemotaxis

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