Boundary Value Problems for Linear PDEs with Variable Coefficients

2004/12/01 by A. S. Fokas, Fokas, A. S.
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.math/0412029

arxiv created 2004/12/01 · openalex publication_date 2004/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new method is introduced for studying boundary value problems for a class of linear PDEs with \it variable coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs with \it constant coefficients. As illustrative examples the following boundary value problems are solved: (a) A Dirichlet and a Neumann problem on the half line for the time-dependent Schrödinger equation with a space dependent potential. (b) A Poincaré problem on the quarter plane for a variable coefficient eneralisation of the Laplace equation.

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