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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2408.02471 |
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| _version_ | 1866914900691910656 |
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| author | Sánchez, Claudia Fonte Mischler, Stéphane |
| author_facet | Sánchez, Claudia Fonte Mischler, Stéphane |
| contents | We consider the nonlinear Voltage-Conductance kinetic equation arising in neuroscience. We establish the existence of solutions in a weighted $L^\infty$ framework in a weak interaction regime. We also prove the linear asymptotic exponential stability of the steady state making constructive a recent estimate of Xu'an Dou et al. (2023). Both results are based in a fundamental way on some ultracontractivity property of theflow associated to the linear (possibly time dependent) Voltage-Conductance kinetic equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02471 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Voltage-Conductance kinetic equation Sánchez, Claudia Fonte Mischler, Stéphane Analysis of PDEs We consider the nonlinear Voltage-Conductance kinetic equation arising in neuroscience. We establish the existence of solutions in a weighted $L^\infty$ framework in a weak interaction regime. We also prove the linear asymptotic exponential stability of the steady state making constructive a recent estimate of Xu'an Dou et al. (2023). Both results are based in a fundamental way on some ultracontractivity property of theflow associated to the linear (possibly time dependent) Voltage-Conductance kinetic equation. |
| title | On the Voltage-Conductance kinetic equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.02471 |