Initial-boundary value problems for linear PDEs with variable coefficients

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-...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society Vol. 143; no. 1; pp. 221 - 242
Main Authors: TREHARNE, P. A., FOKAS, A. S.
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.07.2007
Subjects:
Boundary value problems
Linear equations
Mathematical analysis
Mathematical problems
Partial differential equations
ISSN:0305-0041, 1469-8064
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:istex:DB4554AC2229377A6627A6602F997AEE4EF3C697
ArticleID:00008
ark:/67375/6GQ-3XF2NZB5-Q
PII:S0305004107000084
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004107000084