边值问题
数学
偏微分方程
变量(数学)
应用数学
数学分析
价值(数学)
初值问题
统计
作者
P. A. Treharne,A. S. Fokas
出处
期刊:Mathematical proceedings of the Cambridge Philosophical Society
[Cambridge University Press]
日期:2007-07-01
卷期号:143 (1): 221-242
被引量:7
标识
DOI:10.1017/s0305004107000084
摘要
Abstract A new approach for studying initial-boundary value problems for linear partial differential equations (PDEs) with variable coefficients was introduced recently by the second author, and was applied to PDEs involving second order derivatives. Here, we extend this approach further to solve an initial-boundary value problem for a third-order evolution PDE with a space-dependent coefficient. The analysis is presented in such a way that it can be applied to PDEs with higher derivatives, and thus provides a method for solving initial-boundary value problems for a certain class of linear evolution equations with variable coefficients of arbitrary order.
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