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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2408.02471 |
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- 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.