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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
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Official URL: https://doi.org/10.1137/16M110808X
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 | |||||||||
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| 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 | |||||||||
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| 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 | |||||||||
| RIOXX Funder/Project Grant: |
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