Existence and uniqueness of maximal strong solution of a 1d blood flow in a network of vessels

Debayan Maity (1) , Jean-Pierre Raymond (2) , Arnab Roy (3)

1 TIFR-CAM - Center for Applicable Mathematics [Bangalore]
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 IM / CAS - Institute of Mathematics of the Czech Academy of Science

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.

Domaines: Equations aux dérivées partielles [math.AP]

Debayan Maity, Jean-Pierre Raymond, Arnab Roy. Existence and uniqueness of maximal strong solution of a 1d blood flow in a network of vessels. 2020. ⟨hal-02912208⟩