| Abstract: | Motivated by the desire to model the entry of 1,25D into a cell by receptor mediated endocytosis, we have formulated the problem as the dynamics of a bilayer membrane. We have discussed setting the problem as a variational problem using the Helfrich modeling of the bilayer in terms of the free energy. Using a Lagrangian formulation we arrive at the Euler–Lagrange equations for the system. The model we have used depends on the amount of reagent in the neighborhood of the upper membrane. The problem thereby reduces to a moving boundary problem, which is dependent on a diffusion equation for a region changing with time. In order to solve this problem we seek the correct Neumann function for this altered. This is accomplished by deriving a Hadamard variational formula for the diffusion equation. We also offer an iterative procedure for solving this non-linear problem. |
