Conditionally integrable nonlinear diffusion with diffusivity 1/u
journal contributionposted on 14.01.2021, 05:22 by Philip BroadbridgePhilip Broadbridge, Joanna M Goard
© 2019 by the authors.
An explicit mapping is given from the space of general complex meromorphic functions to a space of special time-dependent solutions of the 1 + 2-dimensional nonlinear diffusion equation with diffusivity depending on concentration as D=1/u. These solutions have constant-flux boundary conditions. Some simple examples are constructed, including that of a line source enclosed by a cylindrical barrier. This has direct application to electron diffusion in a laser-heated plasma.