Asymptotic analysis of a doubly nonlinear diffusion equation
We investigate the doubly nonlinear diffusion equation ∂u/∂t=1/n ∇.(u^m│∇u│^n-1) ∇u) and the same equation expressed in terms of a `pressure' variable. We classify various classes of compacted supported solutions, as well as finite-mass solutions that decay algebraically at infinity. A numbe...
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| Format: | Article |
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Elsevier
2016
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| Online Access: | https://eprints.nottingham.ac.uk/33229/ |
| _version_ | 1848794588684222464 |
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| author | King, John R. |
| author_facet | King, John R. |
| author_sort | King, John R. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We investigate the doubly nonlinear diffusion equation
∂u/∂t=1/n ∇.(u^m│∇u│^n-1) ∇u) and the same equation expressed in terms of a `pressure' variable. We classify various classes of compacted supported solutions, as well as finite-mass solutions that decay algebraically at infinity. A number of novel phenomena are identified, particularly for n<0, that seem to us worthy of further mathematical investigation. |
| first_indexed | 2025-11-14T19:18:35Z |
| format | Article |
| id | nottingham-33229 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:18:35Z |
| publishDate | 2016 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-332292024-08-15T15:18:55Z https://eprints.nottingham.ac.uk/33229/ Asymptotic analysis of a doubly nonlinear diffusion equation King, John R. We investigate the doubly nonlinear diffusion equation ∂u/∂t=1/n ∇.(u^m│∇u│^n-1) ∇u) and the same equation expressed in terms of a `pressure' variable. We classify various classes of compacted supported solutions, as well as finite-mass solutions that decay algebraically at infinity. A number of novel phenomena are identified, particularly for n<0, that seem to us worthy of further mathematical investigation. Elsevier 2016-06-01 Article PeerReviewed King, John R. (2016) Asymptotic analysis of a doubly nonlinear diffusion equation. Nonlinear Analysis: Theory, Methods & Applications, 138 . pp. 253-276. ISSN 0362-546X Nonlinear diffusion; asymptotic analysis; moving boundary problems; image analysis http://www.sciencedirect.com/science/article/pii/S0362546X15004125 doi:10.1016/j.na.2015.12.003 doi:10.1016/j.na.2015.12.003 |
| spellingShingle | Nonlinear diffusion; asymptotic analysis; moving boundary problems; image analysis King, John R. Asymptotic analysis of a doubly nonlinear diffusion equation |
| title | Asymptotic analysis of a doubly nonlinear diffusion equation |
| title_full | Asymptotic analysis of a doubly nonlinear diffusion equation |
| title_fullStr | Asymptotic analysis of a doubly nonlinear diffusion equation |
| title_full_unstemmed | Asymptotic analysis of a doubly nonlinear diffusion equation |
| title_short | Asymptotic analysis of a doubly nonlinear diffusion equation |
| title_sort | asymptotic analysis of a doubly nonlinear diffusion equation |
| topic | Nonlinear diffusion; asymptotic analysis; moving boundary problems; image analysis |
| url | https://eprints.nottingham.ac.uk/33229/ https://eprints.nottingham.ac.uk/33229/ https://eprints.nottingham.ac.uk/33229/ |