2025/12/01 by Marjeta Kramar Fijavž, Delio Mugnolo, Kramar, Marjeta +3
Engineering · Mathematics · #47B65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Primary 47D06 #Secondary 35K99 #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2512.01719
openalex publication_date 2025/12/01 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
The theory of one-sided coupled operator matrices, recently introduced by K.-J. Engel, is an abstract framework for concrete initial value problems and allows complete information on well-posedness, and stability of solutions. These notes are meant as a survey on this rich theory, with a particular stress on applications to initial-boundary value problems with unbounded boundary feedbacks. A diffusion-transport system with dynamical boundary conditions is discussed, and its well-posedness and various other properties are investigated. As a by-product, the well-posedness of a wave equation with dynamical boundary condition is also obtained.