On diffusion in an external field and the adjoint source problem
Author:
Julian Keilson
Journal:
Quart. Appl. Math. 12 (1955), 435-438
MSC:
Primary 35.0X
DOI:
https://doi.org/10.1090/qam/67326
MathSciNet review:
67326
Full-text PDF Free Access
Abstract |
Similar Articles |
Additional Information
Abstract: If diffusion in an external field is described by $\partial \rho /\partial t = D{\nabla ^2}\rho - \rho /\tau - \nabla \cdot \left ( {F\left ( r \right )\rho } \right )$, the function $\gamma \left ( {{r_0}} \right )$ describing the probability that a particle at ${r_0}$ will reach a collector surface before decaying or being absorbed by other surfaces satisfies the equation $D{\nabla ^2}\gamma - \gamma /\tau + F\left ( r \right ) \cdot \nabla \gamma = 0$. This equation has no singularity to disturb any geometric symmetry available. Boundary conditions on $\gamma \left ( r \right )$ at the collector surface and other influencing surfaces are derived and shown to be independent of the external field. The boundary conditions at the secondary surfaces are homogeneous. The collector surface boundary condition is inhomogeneous.
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
35.0X
Retrieve articles in all journals
with MSC:
35.0X
Additional Information
Article copyright:
© Copyright 1955
American Mathematical Society