Existence Result For a Model Coupling a Quasi-Linear Parabolic Equation\n and a Linear Hyperbolic System

2022/09/27 by Djamal Ait-Akli, Ait-Akli, Djamal
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2209.13554

openalex publication_date 2022/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove globally-in-time existence of solution for a problem coupling the\nlinear Lam 'e system and the quasi-linear Stokes equation. A solution of this\nglobal coupled problem is viewed as the fixed point of some non-linear operator\nT. We construct, using a regularization procedure, a sequence\n(T^\ε)_\ε of auxiliary approximating compact operators. Then we\nestablish, using a combination of Banach and Schaeffer fixed point theorems,\nthe existence of fixed points to every operator T^\ε. Finally we prove\nthat these fixed points converge to the fixed point of T\n

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