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Fokas method for a multi-domain linear reaction-diffusion equation with discontinuous diffusivity

M. Asvestas, Sifalakis Anastasios, Papadopoulou Eleni, Saridakis Ioannis

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URIhttp://purl.tuc.gr/dl/dias/4384927C-2779-45D8-8E73-4919F472845D-
Identifierhttp://iopscience.iop.org/article/10.1088/1742-6596/490/1/012143/pdf-
Languageen-
Extent4 pagesen
TitleFokas method for a multi-domain linear reaction-diffusion equation with discontinuous diffusivityen
CreatorM. Asvestasen
CreatorSifalakis Anastasiosen
CreatorΣηφαλακης Αναστασιοςel
CreatorPapadopoulou Elenien
CreatorΠαπαδοπουλου Ελενηel
CreatorSaridakis Ioannisen
CreatorΣαριδακης Ιωαννηςel
PublisherIOP Publishingen
Content SummaryMotivated by proliferation-diffusion mathematical models for studying highly diffusive brain tumors, that also take into account the heterogeneity of the brain tissue, in the present work we consider a multi-domain linear reaction-diffusion equation with a discontinuous diffusion coefficient. For the solution of the problem at hand we implement Fokas transform method by directly following, and extending in this way, our recent work for a white-gray- white matter brain model pertaining to high grade gliomas. Fokas’s novel approach for the solution of linear PDE problems, yields novel integral representations of the solution in the complex plane that, for appropriately chosen integration contours, decay exponentially fast and converge uniformly at the boundaries. Combining these method-inherent advantages with simple numerical quadrature rules, we produce an efficient method, with fast decaying error properties, for the solution of the discontinuous reaction-diffusion problem.en
Type of ItemΠλήρης Δημοσίευση σε Συνέδριοel
Type of ItemConference Full Paperen
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2015-10-16-
Date of Publication2013-
SubjectGreek mathematicsen
Subjectmathematics greeken
Subjectgreek mathematicsen
Bibliographic Citation M. Asvestas, A. Sifalakis, E. Papadopoulou, Y. Saridakis. (2013). Fokas method for a multi- domain linear reaction-diffusion equation with discontinuous diffusivity. Presented at Proceedings of IC- MSQUARE Conference on Mathematical Modeling in Physical Science. [online]. Available:http://iopscience.iop.org/article/10.1088/1742-6596/490/1/012143/pdfen

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