Diffusion-aggregation processes with mono-stable reaction terms
This paper analyses front propagation of the equation $u_\tau=[D(u)v_x]_x +f(v) \;\;\; \tau < 0, x \in \mathbb{R}$ where $f$ is a monostable (ie Fisher-type) nonlinear reaction term and $D(v)$ changes its sign once, from positive to negative values,in the interval $ v \in[0,1]$ where the...
| मुख्य लेखकों: | , , , |
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| स्वरूप: | Journal article |
| प्रकाशित: |
2006
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| _version_ | 1826302829039452160 |
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| author | Maini, P Malaguti, L Marcelli, C Matucci, S |
| author_facet | Maini, P Malaguti, L Marcelli, C Matucci, S |
| author_sort | Maini, P |
| collection | OXFORD |
| description | This paper analyses front propagation of the equation $u_\tau=[D(u)v_x]_x +f(v) \;\;\; \tau < 0, x \in \mathbb{R}$ where $f$ is a monostable (ie Fisher-type) nonlinear reaction term and $D(v)$ changes its sign once, from positive to negative values,in the interval $ v \in[0,1]$ where the process is studied. This model equation accounts for simultaneous diffusive and aggregative behaviors of a population dynamic depending on the population density $v$ at time $\tau$ and position $x$. The existence of infinitely many travelling wave solutions is proven. These fronts are parametrized by their wave speed and monotonically connect the stationary states u = 0 and v = 1. In the degenerate case, i.e. when D(0) and/or D(1) = 0, sharp profiles appear, corresponding to the minimum wave speed. They also have new behaviors, in addition to those already observed in diffusive models, since they can be right compactly supported, left compactly supported, or both. The dynamics can exhibit, respectively, the phenomena of finite speed of propagation, finite speed of saturation, or both. |
| first_indexed | 2024-03-07T05:53:21Z |
| format | Journal article |
| id | oxford-uuid:e9a8e4f5-107a-45d6-921f-fe66fef22ac8 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:53:21Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:e9a8e4f5-107a-45d6-921f-fe66fef22ac82022-03-27T10:55:56ZDiffusion-aggregation processes with mono-stable reaction termsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e9a8e4f5-107a-45d6-921f-fe66fef22ac8Mathematical Institute - ePrints2006Maini, PMalaguti, LMarcelli, CMatucci, SThis paper analyses front propagation of the equation $u_\tau=[D(u)v_x]_x +f(v) \;\;\; \tau < 0, x \in \mathbb{R}$ where $f$ is a monostable (ie Fisher-type) nonlinear reaction term and $D(v)$ changes its sign once, from positive to negative values,in the interval $ v \in[0,1]$ where the process is studied. This model equation accounts for simultaneous diffusive and aggregative behaviors of a population dynamic depending on the population density $v$ at time $\tau$ and position $x$. The existence of infinitely many travelling wave solutions is proven. These fronts are parametrized by their wave speed and monotonically connect the stationary states u = 0 and v = 1. In the degenerate case, i.e. when D(0) and/or D(1) = 0, sharp profiles appear, corresponding to the minimum wave speed. They also have new behaviors, in addition to those already observed in diffusive models, since they can be right compactly supported, left compactly supported, or both. The dynamics can exhibit, respectively, the phenomena of finite speed of propagation, finite speed of saturation, or both. |
| spellingShingle | Maini, P Malaguti, L Marcelli, C Matucci, S Diffusion-aggregation processes with mono-stable reaction terms |
| title | Diffusion-aggregation processes with mono-stable reaction terms |
| title_full | Diffusion-aggregation processes with mono-stable reaction terms |
| title_fullStr | Diffusion-aggregation processes with mono-stable reaction terms |
| title_full_unstemmed | Diffusion-aggregation processes with mono-stable reaction terms |
| title_short | Diffusion-aggregation processes with mono-stable reaction terms |
| title_sort | diffusion aggregation processes with mono stable reaction terms |
| work_keys_str_mv | AT mainip diffusionaggregationprocesseswithmonostablereactionterms AT malagutil diffusionaggregationprocesseswithmonostablereactionterms AT marcellic diffusionaggregationprocesseswithmonostablereactionterms AT matuccis diffusionaggregationprocesseswithmonostablereactionterms |