Constructing Solutions to Two-Way Diffusion Problems
Abstract
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces several technical challenges. Existence and uniqueness theorems have been established in the literature under various assumptions; however, calculating solutions in practice has proven difficult. Here we present one possible means of practical calculation. By formulating the problem in terms of projection operators, we derive a formal sum for the solution whose terms are readily calculated. We demonstrate the validity of this approach for a variety of physical problems, with focus on a periodic problem from the field of active matter.
Cite
@article{arxiv.1808.04665,
title = {Constructing Solutions to Two-Way Diffusion Problems},
author = {Caleb G. Wagner and Richard Beals},
journal= {arXiv preprint arXiv:1808.04665},
year = {2019}
}
Comments
Published in J. Phys. A: Math. Theor