Existence and Asymptotic Behavior of Solutions to a Quasilinear Hyperbolic-Parabolic Model of Vasculogenesis

2011/12/08 by Cristiana Di Russo, Di Russo, Cristiana, Alice Sepe +1 · 1 citation
Mathematics · #35B40 #35L45 #35L60 #92C15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP #msc:35B40 #msc:35L45 #msc:35L60 #msc:92C15

paper · pdf · doi:10.48550/arxiv.1112.1940

27 pages

openalex publication_date 2011/12/08 · arxiv created 2011/12/13 · arxiv updated 2011/12/14 · openalex created_date 2022/09/21 · openalex updated_date 2026/07/28

Abstract

We consider a hyperbolic-parabolic model of vasculogenesis in the multidimensional case. For this system we show the global existence of smooth solutions to the Cauchy problem, using suitable energy estimates. Since this model does not enter in the classical framework of dissipative problems, we analyze it combining the features of the hyperbolic and the parabolic parts. Moreover we study the asymptotic behavior of those solutions showing their decay rates by means of detailed analysis of the Green function for the linearized problem.

Citations

• Global Existence of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy
• On Relaxation Hyperbolic Systems Violating the Shizuta–Kawashima Condition

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