TY - JOUR
TI - Boundary behavior of the solution to the linear Korteweg-De Vries equation on the half line
AU - Chatziafratis, A.
AU - Kamvissis, S.
AU - Stratis, I.G.
JO - Studies in Applied Mathematics
PY - 2023
VL - 150
TODO - 2
SP - 339-379
PB - John Wiley and Sons Inc
SN - 0022-2526, 1467-9590
TODO - 10.1111/sapm.12542
TODO - Initial value problems;  Mathematical transformations, Classical solutions;  Ehrenpreis–palamodov representation;  Fokas formula;  Forced linearized korteweg-de vrie equation on the half-line;  Half-line;  Korteweg-de Vries-equation;  Long-space estimate;  Mixed initial-boundary value problem;  Smoothness up to the boundary;  Transform methods;  Unified transform method, Korteweg-de Vries equation
TODO - In this paper, we consider the solution to the linear Korteweg-De Vries (KdV) equation, both homogeneous and forced, on the quadrant (Formula presented.) via the unified transform method of Fokas and we provide a complete rigorous study of the integrals of the formula provided by the method, especially focusing on the explicit verification of the considered initial-boundary-value problems (IBVPs), with generic data, as well as on the uniform convergence of all its derivatives, as (Formula presented.) approaches the boundary of the quadrant, and their rapid decay as (Formula presented.). © 2022 Wiley Periodicals LLC.
ER -