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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.18400 |
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| _version_ | 1866908464645668864 |
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| author | Álvarez-Caudevilla, Pablo Brändle, Cristina González-Pereiro, Fermin |
| author_facet | Álvarez-Caudevilla, Pablo Brändle, Cristina González-Pereiro, Fermin |
| contents | This work investigates a model describing the interaction of two species in habiting separate but adjacent areas. These populations are governed by a system of
equations that account for spatial variations in growth rates and the effects of crowding.
A key feature is the presence of areas within each domain where resources are unlimited
and crowding effects are absent. The species interact solely through a common bound ary interface, which is modeled by asymmetric Kedem-Katchalsky boundary conditions.
The paper provides existence, non-existence, and behavior of positive solutions for the
system. It is shown that a unique positive population distribution exists when one of the
growth rate parameters falls within a specific range defined by two critical values. One of
these critical values represents a bifurcation point where the population can emerge from
extinction, while the other is determined by the characteristics of the refuge areas. The
study also examines how the populations behave as the growth parameter approaches the
upper critical value. This analysis reveals the phenomenon of non-simultaneous blow-up,
where one population component can grow infinitely large within its refuge zone while
the other remains bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymmetric Kedem-Katchalsky boundary conditions for systems with spatial heterogeneities Álvarez-Caudevilla, Pablo Brändle, Cristina González-Pereiro, Fermin Analysis of PDEs This work investigates a model describing the interaction of two species in habiting separate but adjacent areas. These populations are governed by a system of equations that account for spatial variations in growth rates and the effects of crowding. A key feature is the presence of areas within each domain where resources are unlimited and crowding effects are absent. The species interact solely through a common bound ary interface, which is modeled by asymmetric Kedem-Katchalsky boundary conditions. The paper provides existence, non-existence, and behavior of positive solutions for the system. It is shown that a unique positive population distribution exists when one of the growth rate parameters falls within a specific range defined by two critical values. One of these critical values represents a bifurcation point where the population can emerge from extinction, while the other is determined by the characteristics of the refuge areas. The study also examines how the populations behave as the growth parameter approaches the upper critical value. This analysis reveals the phenomenon of non-simultaneous blow-up, where one population component can grow infinitely large within its refuge zone while the other remains bounded. |
| title | Asymmetric Kedem-Katchalsky boundary conditions for systems with spatial heterogeneities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.18400 |