2025/02/12 by Dalal Daw, Daw, Dalal, Marko Nedeljkov +2
Earth and Planetary Sciences · #35G35 #35L65 #35L67 #76L05 #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2502.08329
openalex publication_date 2025/02/12 · openalex created_date 2025/02/15 · openalex updated_date 2026/07/28
The shallow water system with a bed jump describes a fluid flow over a dam, represented by a simple step function with the Riemann initial data is such that the vacuum is on the right-hand side. The main question is whether the fluid will stay on the left-hand side of the dam. After approximating the step function space derivative with a fixed shadow wave, solutions to that problem stay bounded. A proper connection between waves on both sides of the dam, and a unique solution afterward is found by using the maximal dissipation principle.