Existence and uniqueness of maximal strong solution of a 1D blood flow in a network of vessels. (February 2022)

• Record Type: Journal Article
• Authors: Maity, Debayan; Raymond, Jean-Pierre; Roy, Arnab
• Is Part Of: Nonlinear analysis. Volume 63(2022)
• Publication Date: 2022-02
• Subjects: One-dimensional blood flow model -- Viscoelastic vessels -- Strong solutions -- Maximal-in-time solutions -- Uniqueness of solution -- Fluid–structure interaction; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103405
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the well-posedness of a system of one-dimensional partial differential equations modeling blood flows in a network of vessels with viscoelastic walls. We prove the existence and uniqueness of maximal strong solution for this type of hyperbolic/parabolic model. We also prove a stability estimate under suitable nonlinear Robin boundary conditions.