Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption
Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bifurcations occur at particular points in parameter...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2018
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| Online Access: | https://eprints.nottingham.ac.uk/53818/ |
| _version_ | 1848798990324203520 |
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| author | Foster, J.M. Gysbers, P. King, J.R. Pelinovsky, D.E. |
| author_facet | Foster, J.M. Gysbers, P. King, J.R. Pelinovsky, D.E. |
| author_sort | Foster, J.M. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bifurcations occur at particular points in parameter space (characterizing the exponents in the diffusion and absorption terms) where the confluent hypergeometric functions satisfying Kummer's differential equation truncate to finite polynomials. A two-scale asymptotic method is employed to obtain the local dependencies of the self-similar reversing interfaces near the bifurcation points. The asymptotic results are shown to be in excellent agreement with numerical approximations of the self-similar solutions. |
| first_indexed | 2025-11-14T20:28:33Z |
| format | Article |
| id | nottingham-53818 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:28:33Z |
| publishDate | 2018 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-538182019-08-31T04:30:13Z https://eprints.nottingham.ac.uk/53818/ Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption Foster, J.M. Gysbers, P. King, J.R. Pelinovsky, D.E. Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bifurcations occur at particular points in parameter space (characterizing the exponents in the diffusion and absorption terms) where the confluent hypergeometric functions satisfying Kummer's differential equation truncate to finite polynomials. A two-scale asymptotic method is employed to obtain the local dependencies of the self-similar reversing interfaces near the bifurcation points. The asymptotic results are shown to be in excellent agreement with numerical approximations of the self-similar solutions. IOP Publishing 2018-10-30 Article PeerReviewed application/pdf en cc_by_nc_nd https://eprints.nottingham.ac.uk/53818/1/BifurcationsSelfSim_FINAL_CLEAN.pdf Foster, J.M., Gysbers, P., King, J.R. and Pelinovsky, D.E. (2018) Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption. Nonlinearity, 31 (10). pp. 4621-4648. ISSN 0951-7715 http://iopscience.iop.o...0.1088/1361-6544/aad30b doi:10.1088/1361-6544/aad30b doi:10.1088/1361-6544/aad30b |
| spellingShingle | Foster, J.M. Gysbers, P. King, J.R. Pelinovsky, D.E. Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption |
| title | Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption |
| title_full | Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption |
| title_fullStr | Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption |
| title_full_unstemmed | Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption |
| title_short | Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption |
| title_sort | bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption |
| url | https://eprints.nottingham.ac.uk/53818/ https://eprints.nottingham.ac.uk/53818/ https://eprints.nottingham.ac.uk/53818/ |