Work

The Fokas method for evolution partial differential equations

Year: 2025

Type: article

Abstract: In the late 1990s a novel methodology was introduced for solving boundary value problems for linear and integrable nonlinear PDEs. This new approach is known as the Unified Transform or the Fokas method. Here we discuss important developments regarding the implementation of this methodology to evolution PDEs. In particular, we analyze linear PDEs, including the heat equation, the Sobolev-Barenblatt pseudo-parabolic model, the Rubinshtein-Aifantis double-diffusion system, and the linearized Cahn-Hilliard model, as well as certain integrable nonlinear PDEs, like the nonlinear Schrödinger equation. Regarding the latter equation, emphasis is placed on the so-called linearizable boundary conditions, which remarkably, include the well-studied x -periodic initial value problem.

Source: Partial Differential Equations in Applied Mathematics

DOI: 10.1016/j.padiff.2025.101144

Authors: A. Chatziafratis, A.S. Fokas, K. Kalimeris

Institutions: University of Cyprus, Foundation for Research and Technology Hellas, Academy of Athens, University of Cambridge

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,470

OpenAlex ID: W4408252149

FWCI: 15.01

Cites: 115

Cited by: 8

Related to: 10