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Boundary Value Problems for Linear PDEs with Variable Coefficients

A. S. Fokas
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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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A. S. Fokas. 2004-12-01. Boundary Value Problems for Linear PDEs with Variable Coefficients. https://arxiv.org/abs/math/0412029

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