The Airy equation with nonlocal conditions

DOI10.1111/SAPM.12652arXiv2306.11273OpenAlexW4388671798MaRDI QIDQ6440813

Dealton J. Smith, B. Normatov

Publication date: 20 June 2023

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.

Full work available at URL: https://doi.org/10.1111/sapm.12652

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Related Items (1)

Preface: Integrable systems and their applications, celebrating the 70th birthday of Athanassios S. Fokas

This page was built for publication: The Airy equation with nonlocal conditions

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6440813)