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Solvability and asymptotics of the heat equation with mixed variable lateral conditions and applications in the opening of the exocytotic fusion pore in cells
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
University of Birmingham, UK.
2014 (English)In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 79, no 2, 377-392 p.Article in journal (Refereed) Published
Abstract [en]

We investigate a mixed problem with variable lateral conditions for the heat equation that arises in modelling exocytosis, i.e. the opening of a cell boundary in specific biological species for the release of certain molecules to the exterior of the cell. The Dirichlet condition is imposed on a surface patch of the boundary and this patch is occupying a larger part of the boundary as time increases modelling where the cell is opening (the fusion pore), and on the remaining part, a zero Neumann condition is imposed (no molecules can cross this boundary). Uniform concentration is assumed at the initial time. We introduce a weak formulation of this problem and show that there is a unique weak solution. Moreover, we give an asymptotic expansion for the behaviour of the solution near the opening point and for small values in time. We also give an integral equation for the numerical construction of the leading term in this expansion.

Place, publisher, year, edition, pages
Oxford University Press, 2014. Vol. 79, no 2, 377-392 p.
Keyword [en]
exocytosis, heat conduction, mixed problem
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-86222DOI: 10.1093/imamat/hxs071ISI: 000333272600010OAI: diva2:575795
Available from: 2012-12-11 Created: 2012-12-11 Last updated: 2014-04-25

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Kozlov, Vladimir
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