Year: 2019
Type: article
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.
Authors: Caleb G Wagner, Richard Beals
Institutions: Brandeis University, Yale University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2885829877