The Airy equation with nonlocal conditions

2023/06/20 by Бекзод Normatov, David A. Smith, Normatov, Bekzod +1
Mathematics · Physics and Astronomy · #34B10 #35C15 #35E15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2306.11273

openalex publication_date 2023/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a third order dispersive linear evolution equation on the finite interval subject to an initial condition and inhomogeneous boundary conditions but, in place of one of the three boundary conditions that would typically be imposed, we use a nonlocal condition, which specifies a weighted integral of the solution over the spatial interval. Via adaptations of the Fokas transform method (or unified transform method), we obtain a solution representation for this problem. We also study the time periodic analogue of this problem, and thereby obtain long time asymptotics for the original problem with time periodic boundary and nonlocal data.

Related

• Long time behaviour of solutions to non-local and non-linear dispersion problems
• The diffusion equation with nonlocal data
• Revivals, or the Talbot effect, for the Airy equation
• The role of periodicity in the solution of third order boundary value problems
• Fokas method for linear convection-diffusion equation with time-dependent coefficients and its extension to other evolution equations