An approximation to a sharp type solution of a density-dependent diffusion equation
In this paper, we use a perturbation method to obtain an approximation to a saddle-saddle heteroclinic trajectory of an autonomous system of ordinary differential equations (ODEs) arising in the equation $u_t= [(u+\epsilon u^2)u_x]_x+u(1-u)$ in the case of travelling wave solutions (t.w.s.): $ u(x,t...
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Format: | Journal article |
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1994
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author | Sánchez-Garduño, F Maini, P |
author_facet | Sánchez-Garduño, F Maini, P |
author_sort | Sánchez-Garduño, F |
collection | OXFORD |
description | In this paper, we use a perturbation method to obtain an approximation to a saddle-saddle heteroclinic trajectory of an autonomous system of ordinary differential equations (ODEs) arising in the equation $u_t= [(u+\epsilon u^2)u_x]_x+u(1-u)$ in the case of travelling wave solutions (t.w.s.): $ u(x,t) = \phi (x - ct)$. We compare the approximate form of the solution profile and speed thus obtained with the actual solution of the full model and the calculated speed, respectively. |
first_indexed | 2024-03-07T02:16:47Z |
format | Journal article |
id | oxford-uuid:a2856105-6931-4a48-9240-2a7da9e65663 |
institution | University of Oxford |
last_indexed | 2024-03-07T02:16:47Z |
publishDate | 1994 |
record_format | dspace |
spelling | oxford-uuid:a2856105-6931-4a48-9240-2a7da9e656632022-03-27T02:20:41ZAn approximation to a sharp type solution of a density-dependent diffusion equationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a2856105-6931-4a48-9240-2a7da9e65663Mathematical Institute - ePrints1994Sánchez-Garduño, FMaini, PIn this paper, we use a perturbation method to obtain an approximation to a saddle-saddle heteroclinic trajectory of an autonomous system of ordinary differential equations (ODEs) arising in the equation $u_t= [(u+\epsilon u^2)u_x]_x+u(1-u)$ in the case of travelling wave solutions (t.w.s.): $ u(x,t) = \phi (x - ct)$. We compare the approximate form of the solution profile and speed thus obtained with the actual solution of the full model and the calculated speed, respectively. |
spellingShingle | Sánchez-Garduño, F Maini, P An approximation to a sharp type solution of a density-dependent diffusion equation |
title | An approximation to a sharp type solution of a density-dependent diffusion equation |
title_full | An approximation to a sharp type solution of a density-dependent diffusion equation |
title_fullStr | An approximation to a sharp type solution of a density-dependent diffusion equation |
title_full_unstemmed | An approximation to a sharp type solution of a density-dependent diffusion equation |
title_short | An approximation to a sharp type solution of a density-dependent diffusion equation |
title_sort | approximation to a sharp type solution of a density dependent diffusion equation |
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