A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term
In this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x + g(u)$ for different density-dependent diffusion coefficients D and kinetic part g. These include the no...
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| Format: | Journal article |
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1996
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| author | Sánchez-Garduño, F Maini, P Kappos, E |
| author_facet | Sánchez-Garduño, F Maini, P Kappos, E |
| author_sort | Sánchez-Garduño, F |
| collection | OXFORD |
| description | In this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x + g(u)$ for different density-dependent diffusion coefficients D and kinetic part g. These include the non-linear degenerate generalized Fisher-KPP and the Nagumo equations. Also, we consider an equation whose diffusion coefficient changes sign as the diffusive substance increases. This describes a diffusive-aggregative process. In this case the travelling wave solutions are explored and the ill-posedness of two boundary-value problems associated with the above equation is stated. |
| first_indexed | 2024-03-06T19:33:38Z |
| format | Journal article |
| id | oxford-uuid:1e4f980f-fcbd-4bb0-b43b-5b6c3fc56e5e |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:33:38Z |
| publishDate | 1996 |
| record_format | dspace |
| spelling | oxford-uuid:1e4f980f-fcbd-4bb0-b43b-5b6c3fc56e5e2022-03-26T11:15:33ZA review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion termJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1e4f980f-fcbd-4bb0-b43b-5b6c3fc56e5eMathematical Institute - ePrints1996Sánchez-Garduño, FMaini, PKappos, EIn this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x + g(u)$ for different density-dependent diffusion coefficients D and kinetic part g. These include the non-linear degenerate generalized Fisher-KPP and the Nagumo equations. Also, we consider an equation whose diffusion coefficient changes sign as the diffusive substance increases. This describes a diffusive-aggregative process. In this case the travelling wave solutions are explored and the ill-posedness of two boundary-value problems associated with the above equation is stated. |
| spellingShingle | Sánchez-Garduño, F Maini, P Kappos, E A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term |
| title | A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term |
| title_full | A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term |
| title_fullStr | A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term |
| title_full_unstemmed | A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term |
| title_short | A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term |
| title_sort | review on travelling wave solutions of one dimensional reaction diffusion equations with non linear diffusion term |
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