Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/<i>u</i>
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 <inline-formula> <math display="inline"> <...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-06-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/11/6/804 |
| Summary: | 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mi>u</mi></mrow></semantics></math></inline-formula>. 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. |
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| ISSN: | 2073-8994 |