Uniform asymptotic approximation of diffusion to a small target.

@article{Isaacson2013UniformAA,
  title={Uniform asymptotic approximation of diffusion to a small target.},
  author={Samuel A. Isaacson and Jay M. Newby},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={88 1},
  pages={012820}
}
The problem of the time required for a diffusing molecule, within a large bounded domain, to first locate a small target is prevalent in biological modeling. Here we study this problem for a small spherical target. We develop uniform in time asymptotic expansions in the target radius of the solution to the corresponding diffusion equation. Our approach is based on combining expansions of a long-time approximation of the solution, involving the first eigenvalue and eigenfunction of the Laplacian… CONTINUE READING