Boundary value problems for third-order linear PDEs in time-dependent domains
Pelloni, B. (2008) Boundary value problems for third-order linear PDEs in time-dependent domains. Inverse Problems, 24 (1). 015004. ISSN 0266-5611
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To link to this article DOI: 10.1088/0266-5611/24/1/015004
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.