A NON-LINEAR DEGENERATE EQUATION FOR DIRECT AGGREGATION AND TRAVELING WAVE DYNAMICS
The gregarious behavior of individuals of populations is an important factor in avoiding predators or for reproduction. Here, by using a random biased walk approach, we build a model which, after a transformation, takes the general form ut = [D(u)ux]x + g(u). The model involves a density-dependent n...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2010
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| _version_ | 1797072436907212800 |
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| author | Sanchez-Garduno, F Maini, P Perez-Velazquez, J |
| author_facet | Sanchez-Garduno, F Maini, P Perez-Velazquez, J |
| author_sort | Sanchez-Garduno, F |
| collection | OXFORD |
| description | The gregarious behavior of individuals of populations is an important factor in avoiding predators or for reproduction. Here, by using a random biased walk approach, we build a model which, after a transformation, takes the general form ut = [D(u)ux]x + g(u). The model involves a density-dependent non-linear diffusion coefficient D whose sign changes as the population density u increases. For negative values of D aggregation occurs, while dispersion occurs for positive values of D. We deal with a family of degenerate negative diffusion equations with logistic-like growth rate g. We study the one-dimensional traveling wave dynamics for these equations and illustrate our results with a couple of examples. A discussion of the ill-posedness of the partial differential equation problem is included. |
| first_indexed | 2024-03-06T23:07:37Z |
| format | Journal article |
| id | oxford-uuid:64638aaa-0a9c-421f-95b9-d85c1e9ca205 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:07:37Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:64638aaa-0a9c-421f-95b9-d85c1e9ca2052022-03-26T18:18:38ZA NON-LINEAR DEGENERATE EQUATION FOR DIRECT AGGREGATION AND TRAVELING WAVE DYNAMICSJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:64638aaa-0a9c-421f-95b9-d85c1e9ca205EnglishSymplectic Elements at Oxford2010Sanchez-Garduno, FMaini, PPerez-Velazquez, JThe gregarious behavior of individuals of populations is an important factor in avoiding predators or for reproduction. Here, by using a random biased walk approach, we build a model which, after a transformation, takes the general form ut = [D(u)ux]x + g(u). The model involves a density-dependent non-linear diffusion coefficient D whose sign changes as the population density u increases. For negative values of D aggregation occurs, while dispersion occurs for positive values of D. We deal with a family of degenerate negative diffusion equations with logistic-like growth rate g. We study the one-dimensional traveling wave dynamics for these equations and illustrate our results with a couple of examples. A discussion of the ill-posedness of the partial differential equation problem is included. |
| spellingShingle | Sanchez-Garduno, F Maini, P Perez-Velazquez, J A NON-LINEAR DEGENERATE EQUATION FOR DIRECT AGGREGATION AND TRAVELING WAVE DYNAMICS |
| title | A NON-LINEAR DEGENERATE EQUATION FOR DIRECT AGGREGATION AND TRAVELING WAVE DYNAMICS |
| title_full | A NON-LINEAR DEGENERATE EQUATION FOR DIRECT AGGREGATION AND TRAVELING WAVE DYNAMICS |
| title_fullStr | A NON-LINEAR DEGENERATE EQUATION FOR DIRECT AGGREGATION AND TRAVELING WAVE DYNAMICS |
| title_full_unstemmed | A NON-LINEAR DEGENERATE EQUATION FOR DIRECT AGGREGATION AND TRAVELING WAVE DYNAMICS |
| title_short | A NON-LINEAR DEGENERATE EQUATION FOR DIRECT AGGREGATION AND TRAVELING WAVE DYNAMICS |
| title_sort | non linear degenerate equation for direct aggregation and traveling wave dynamics |
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