2022/12/20 by Igor Leite Freire, Freire, Igor Leite
Mathematics · Physics and Astronomy · #35A01 #35Q35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2212.10034
openalex publication_date 2022/12/20 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28
We consider persistence properties of solutions for a generalised wave equation including vibration in elastic rods and shallow water models, such as the BBM, the Dai's, the Camassa-Holm, and the Dullin-Gottwald-Holm equations, as well as some recent shallow water equations with the Coriolis effect. We establish unique continuation results and exhibit asymptotic profiles for the solutions of the general class considered. From these results we prove the non-existence of non-trivial spatially compactly supported solutions for the equation. As an aftermath, we study the equations earlier mentioned in light of our results for the general class.