Boundary value problems for third-order linear PDEs in time-dependent domains

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Abstract

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.
Original languageEnglish
Article number015004
JournalInverse Problems
Volume24
Issue number1
DOIs
Publication statusPublished - Feb 2008

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