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A coupled ligand-receptor bulk-surface system on a moving domain : well posedness, regularity and convergence to equilibrium

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Alphonse, Amal, Elliott, Charles M. and Terra, Joana (2018) A coupled ligand-receptor bulk-surface system on a moving domain : well posedness, regularity and convergence to equilibrium. SIAM Journal on Mathematical Analysis, 50 (2). pp. 1544-1592. doi:10.1137/16M110808X ISSN 0036-1410.

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Official URL: https://doi.org/10.1137/16M110808X

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Abstract

We prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modeling receptor-ligand dynamics in cells. The nonlinear coupling between the three unknowns is through the Robin boundary condition for the bulk quantity and the right-hand sides of the two surface equations. Our results are new even in the nonmoving setting, and in this case we also show exponential convergence to a steady state. The primary complications in the analysis are indeed the nonlinear coupling and the Robin boundary condition. For the well posedness and essential boundedness of solutions we use several De Giorgi-type arguments, and we also develop some useful estimates to allow us to apply a Steklov averaging technique for time-dependent operators to prove that solutions are strong. Some of these auxiliary results presented in this paper are of independent interest by themselves.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Differential equations, Parabolic, Ligands -- Mathematical models
Journal or Publication Title: SIAM Journal on Mathematical Analysis
Publisher: Society for Industrial and Applied Mathematics
ISSN: 0036-1410
Official Date: 15 March 2018
Dates:
DateEvent
15 March 2018Available
22 November 2017Valid
21 November 2017Accepted
Volume: 50
Number: 2
Page Range: pp. 1544-1592
DOI: 10.1137/16M110808X
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 24 November 2017
Date of first compliant Open Access: 15 May 2018
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
Platform grant 3117 University of Warwickhttp://dx.doi.org/10.13039/501100000741
Wolfson Research Merit AwardUNSPECIFIEDhttp://dx.doi.org/10.13039/501100000288
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