A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations
In this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type for the degenerate (at u = 0) parabolic equation $u_1 = [D(u)u_x]_x + g(u)$ where D is a strictly increasing function and g is a function which generalizes the kinetic part of the classical Fisher-KPP equ...
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| Fformat: | Journal article |
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1996
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| _version_ | 1826342847718096896 |
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| author | Sánchez-Garduño, F Kappos, E Maini, P |
| author_facet | Sánchez-Garduño, F Kappos, E Maini, P |
| author_sort | Sánchez-Garduño, F |
| collection | OXFORD |
| description | In this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type for the degenerate (at u = 0) parabolic equation $u_1 = [D(u)u_x]_x + g(u)$ where D is a strictly increasing function and g is a function which generalizes the kinetic part of the classical Fisher-KPP equation. The original problem is transformed into the proper travelling-wave variables, and then a shooting argument is used to show the existence of a saddle-saddle heteroclinic trajectory for a critical value, c*>0, of the speed c of an autonomous system of ordinary differential equations. Associated with this connection is a sharp-type solution of the nonlinear partial differential equation. |
| first_indexed | 2024-03-07T06:47:57Z |
| format | Journal article |
| id | oxford-uuid:fb7fc28e-f91c-4254-a2e8-be4392ddcfd1 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:47:57Z |
| publishDate | 1996 |
| record_format | dspace |
| spelling | oxford-uuid:fb7fc28e-f91c-4254-a2e8-be4392ddcfd12022-03-27T13:14:17ZA shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fb7fc28e-f91c-4254-a2e8-be4392ddcfd1Mathematical Institute - ePrints1996Sánchez-Garduño, FKappos, EMaini, PIn this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type for the degenerate (at u = 0) parabolic equation $u_1 = [D(u)u_x]_x + g(u)$ where D is a strictly increasing function and g is a function which generalizes the kinetic part of the classical Fisher-KPP equation. The original problem is transformed into the proper travelling-wave variables, and then a shooting argument is used to show the existence of a saddle-saddle heteroclinic trajectory for a critical value, c*>0, of the speed c of an autonomous system of ordinary differential equations. Associated with this connection is a sharp-type solution of the nonlinear partial differential equation. |
| spellingShingle | Sánchez-Garduño, F Kappos, E Maini, P A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations |
| title | A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations |
| title_full | A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations |
| title_fullStr | A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations |
| title_full_unstemmed | A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations |
| title_short | A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations |
| title_sort | shooting argument approach to a sharp type solution for nonlinear degenerate fisher kpp equations |
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