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dc.contributor.authorBatal, A.
dc.contributor.authorFokas, A.S.
dc.contributor.authorÖzsari, T.
dc.description.abstractWe obtain solution representation formulae for some linear initial boundary value problems posed on the half space that involve mixed spatial derivative terms via the unified transform method (UTM), also known as the Fokas method. We first implement the method on the second-order parabolic PDEs; in this case one can alternatively eliminate the mixed derivatives by a linear change of variables. Then, we employ the method to biharmonic problems, where it is not possible to eliminate the cross term via a linear change of variables. A basic ingredient of the UTM is the use of certain invariant maps. It is shown here that these maps are well defined provided that certain analyticity issues are appropriately addressed. © 2020 The Author(s).en_US
dc.description.sponsorshipData accessibility. This work does not contain any original experimental data, and all of the results can be generated from the equations provided in the paper. Authors’ contributions. T.Ö. set up the problems and drafted the paper. A.S.F. studied the second-order parabolic equations and initiated the study of the fourth-order heat equation. A.B. and T.Ö. completed the study of the fourth-order heat equation and extended the results to the biharmonic Schrödinger equation. A.B. and T.Ö. prepared the figures. A.B., T.Ö. and A.S.F. revised the text and are accountable for all aspects of the work. Authors are listed in alphabetical order by last name. Competing interests. We declare we have no competing interests. Funding. A.B. and T.Ö.’s research are funded by TÜBİTAK 1001 grant no. 117F449. Acknowledgements. We are deeply grateful to all reviewers for their very kind remarks, their meticulous reviews and thoughtful recommendations.en_US
dc.publisherRoyal Society Publishingen_US
dc.subjectanalyticity issuesen_US
dc.subjectFokas methoden_US
dc.subjectmixed derivativesen_US
dc.subjectunified transform methoden_US
dc.titleFokas method for linear boundary value problems involving mixed spatial derivatives: BVPs with mixed spatial derivativesen_US
dc.relation.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciencesen_US
dc.contributor.departmentIzmir Isntitute of Technologyen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US

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