Boundary Value Problems for Linear PDEs with Variable Coefficients
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
math.MP
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 Schr\"odinger equation with a space dependent potential. (b) A Poincar\'e problem on the quarter plane for a variable coefficient eneralisation of the Laplace equation.
Cite
@article{arxiv.math/0412029,
title = {Boundary Value Problems for Linear PDEs with Variable Coefficients},
author = {A. S. Fokas},
journal= {arXiv preprint arXiv:math/0412029},
year = {2007}
}