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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.00227 |
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| _version_ | 1866909618870943744 |
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| author | Kuwamura, Masataka Teramoto, Takashi Ikeda, Hideo |
| author_facet | Kuwamura, Masataka Teramoto, Takashi Ikeda, Hideo |
| contents | Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of stationary solutions with a single internal transition layer in such reaction-diffusion systems under general assumptions by the singular perturbation theory. Moreover, we present a meaningful model for understanding the existence of an unstable transition layer solution; our numerical simulations show that the unstable solution is a separatrix of the dynamics of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00227 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Single Transition Layer in Mass-Conserving Reaction-Diffusion Systems with Bistable Nonlinearity Kuwamura, Masataka Teramoto, Takashi Ikeda, Hideo Analysis of PDEs 35B25, 35K57 Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of stationary solutions with a single internal transition layer in such reaction-diffusion systems under general assumptions by the singular perturbation theory. Moreover, we present a meaningful model for understanding the existence of an unstable transition layer solution; our numerical simulations show that the unstable solution is a separatrix of the dynamics of the model. |
| title | Single Transition Layer in Mass-Conserving Reaction-Diffusion Systems with Bistable Nonlinearity |
| topic | Analysis of PDEs 35B25, 35K57 |
| url | https://arxiv.org/abs/2305.00227 |