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"> <...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/6/804 |
| _version_ | 1798043125401255936 |
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| author | Philip Broadbridge Joanna M. Goard |
| author_facet | Philip Broadbridge Joanna M. Goard |
| author_sort | Philip Broadbridge |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T22:45:12Z |
| format | Article |
| id | doaj.art-5a4c09ecd19d45cd9e731df815bd6737 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T22:45:12Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-5a4c09ecd19d45cd9e731df815bd67372022-12-22T03:58:48ZengMDPI AGSymmetry2073-89942019-06-0111680410.3390/sym11060804sym11060804Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/<i>u</i>Philip Broadbridge0Joanna M. Goard1Department of Mathematics and Statistics, La Trobe University, Bundoora, VIC 3086, AustraliaSchool of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, AustraliaAn 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.https://www.mdpi.com/2073-8994/11/6/804nonlinear diffusionconditional integrabilityelectron diffusionlaser-heated plasma |
| spellingShingle | Philip Broadbridge Joanna M. Goard Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/<i>u</i> Symmetry nonlinear diffusion conditional integrability electron diffusion laser-heated plasma |
| title | Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/<i>u</i> |
| title_full | Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/<i>u</i> |
| title_fullStr | Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/<i>u</i> |
| title_full_unstemmed | Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/<i>u</i> |
| title_short | Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/<i>u</i> |
| title_sort | conditionally integrable nonlinear diffusion with diffusivity 1 i u i |
| topic | nonlinear diffusion conditional integrability electron diffusion laser-heated plasma |
| url | https://www.mdpi.com/2073-8994/11/6/804 |
| work_keys_str_mv | AT philipbroadbridge conditionallyintegrablenonlineardiffusionwithdiffusivity1iui AT joannamgoard conditionallyintegrablenonlineardiffusionwithdiffusivity1iui |