2013/10/21 by Aimin Huang, Roger Temam, Roger Témam +2
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations #math.AP
paper · pdf · doi:10.48550/arxiv.1310.5757
41 pages
arxiv created 2013/10/21 · openalex publication_date 2013/10/21 · arxiv updated 2013/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we consider linear hyperbolic Initial and Boundary Value Problems (IBVP) in a rectangle (or possibly curvilinear polygonal domains) in both the constant and variable coefficients cases. We use semigroup method instead of Fourier analysis to achieve the well-posedness of the linear hyperbolic system, and we find by diagonalization that there are only two elementary modes in the system which we call hyperbolic and elliptic modes. The hyperbolic system in consideration is either symmetric or Friedrichs-symmetrizable.