Existence and Asymptotic Behavior of Solutions to a Semilinear\n Hyperbolic-Parabolic Model of Chemotaxis

2012/03/24 by Cristiana Di Russo, Di Russo, Cristiana
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #3D Printing in Biomedical Research #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.1203.5404

openalex publication_date 2012/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a general hyperbolic model of chemotaxis in the multidimensional\ncase. For this system we show the global existence of smooth solutions to the\nCauchy problem and we determine their asymptotic behavior. Since this model\ndoes not enter in the classical framework of dissipative problems, we analyze\nit combining the features of the hyperbolic and the parabolic parts and using\ndetailed decay estimates of the Green function.\n

Citations

• A user’s guide to PDE models for chemotaxis

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