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

TL;DR

This paper proves the global existence and analyzes the long-term decay of solutions for a complex hyperbolic-parabolic model of vasculogenesis, combining energy estimates and Green function analysis.

Contribution

It establishes the existence of smooth solutions and characterizes their asymptotic decay, addressing a non-classical hyperbolic-parabolic system in vasculogenesis.

Findings

Global existence of smooth solutions

Decay rates of solutions determined

Green function analysis for linearized problem

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.