Show simple item record

dc.contributor.authorDuong, G. K.
dc.contributor.authorKavallaris, N. I.
dc.contributor.authorZaag, H.
dc.date.accessioned2021-07-03T00:27:33Z
dc.date.available2021-07-03T00:27:33Z
dc.date.issued2021-06-23
dc.identifierdoi: 10.1142/s0218202521500305
dc.identifier.citationMathematical Models and Methods in Applied Sciences, page 1-35
dc.identifier.urihttp://hdl.handle.net/10034/625124
dc.descriptionFrom Crossref journal articles via Jisc Publications Router
dc.descriptionHistory: epub 2021-06-23, issued 2021-06-23
dc.descriptionPublication status: Published
dc.description.abstractIn this paper, we provide a thorough investigation of the blowing up behavior induced via diffusion of the solution of the following non-local problem: [Formula: see text] where [Formula: see text] is a bounded domain in [Formula: see text] with smooth boundary [Formula: see text] such problem is derived as the shadow limit of a singular Gierer–Meinhardt system, Kavallaris and Suzuki [On the dynamics of a non-local parabolic equation arising from the Gierer–Meinhardt system, Nonlinearity (2017) 1734–1761; Non-Local Partial Differential Equations for Engineering and Biology: Mathematical Modeling and Analysis, Mathematics for Industry, Vol. 31 (Springer, 2018)]. Under the Turing type condition [Formula: see text] we construct a solution which blows up in finite time and only at an interior point [Formula: see text] of [Formula: see text] i.e. [Formula: see text] where [Formula: see text] More precisely, we also give a description on the final asymptotic profile at the blowup point [Formula: see text] and thus we unveil the form of the Turing patterns occurring in that case due to driven-diffusion instability. The applied technique for the construction of the preceding blowing up solution mainly relies on the approach developed in [F. Merle and H. Zaag, Reconnection of vortex with the boundary and finite time quenching, Nonlinearity 10 (1997) 1497–1550] and [G. K. Duong and H. Zaag, Profile of a touch-down solution to a nonlocal MEMS model, Math. Models Methods Appl. Sci. 29 (2019) 1279–1348].
dc.publisherWorld Scientific Pub Co Pte Lt
dc.sourcepissn: 0218-2025
dc.sourceeissn: 1793-6314
dc.subjectModelling and Simulation
dc.subjectApplied Mathematics
dc.titleDiffusion-induced blowup solutions for the shadow limit model of a singular Gierer–Meinhardt system
dc.typearticle
dc.date.updated2021-07-03T00:27:33Z


This item appears in the following Collection(s)

Show simple item record