Well-posedness, ill-posedness, and traveling waves for models of pulsatile flow in viscoelastic vessels

DOI10.1007/s00033-022-01874-xOpenAlexW4308494298MaRDI QIDQ2096970

Hyeju Kim, David M. Ambrose

Publication date: 11 November 2022

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.09780

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Physiological flows (76Z05) Bifurcations in context of PDEs (35B32) Traveling wave solutions (35C07)

Related Items

Multiscale Constitutive Framework of One-Dimensional Blood Flow Modeling: Asymptotic Limits and Numerical Methods

Cites Work

• Unnamed Item
• Unnamed Item
• Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation
• A Boussinesq model for pressure and flow velocity waves in arterial segments
• Bifurcation theory. An introduction with applications to partial differential equations
• On some model equations for pulsatile flow in viscoelastic vessels
• Global vortex sheet solutions of Euler equations in the plane
• Sur les ondes de surface de l'eau avec une justification mathématique des équations des ondes en eau peu profonde
• Finite time analyticity for the two and three dimensional Kelvin- Helmholtz instability
• Gain of regularity for equations of KdV type
• A note on a theorem of Nirenberg
• Applied functional analysis. Main principles and their applications
• Local well-posedness of quasi-linear systems generalizing KdV
• Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry
• Modeling blood flow in viscoelastic vessels: the 1D augmented fluid-structure interaction system
• Rigorous asymptotic models of water waves
• An abstract form of the nonlinear Cauchy-Kowalewski theorem
• Bifurcation with a two-dimensional kernel
• Vorticity and Incompressible Flow
• Vortex Sheet Formulations and Initial Value Problems: Analysis and Computing
• A simplified version of the abstract Cauchy-Kowalewski theorem with weak singularities
• Singular Solutions and Ill-Posedness for the Evolution of Vortex Sheets
• Well-Posedness of Vortex Sheets with Surface Tension
• Well-posedness of fully nonlinear KdV-type evolution equations
• Approximation of Polyatomic FPU Lattices by KdV Equations
• Dispersion vs. anti-diffusion: Well-posedness in variable coefficient and quasilinear equations of KdV-type

This page was built for publication: Well-posedness, ill-posedness, and traveling waves for models of pulsatile flow in viscoelastic vessels