Solvability and asymptotics of the heat equation with mixed variable lateral conditions and applications in the opening of the exocytotic fusion pore in cells

B. Tomas Johansson, Vladimir A. Koslov

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Pages (from-to)377-392
Number of pages6
JournalIMA Journal of Applied Mathematics
Volume79
Issue number2
Early online date30 Oct 2012
DOIs
Publication statusPublished - 30 Apr 2014

Keywords

  • exocytosis
  • heat conduction
  • mixed problem

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