On the self-similar stability of the parabolic-parabolic Keller-Segel equation
In: https://hal.science/hal-04267741 ; 2023, 2023
Online
report
Zugriff:
We consider the parabolic-parabolic Keller-Segel equation in the plane and prove the nonlinear exponential stability of the self-similar profile in a quasi parabolic-elliptic regime. We first perform a perturbation argument in order to obtain exponential stability for the semigroup associated to part of the first component of the linearized operator, by exploiting the exponential stability of the linearized operator for the parabolic-elliptic Keller-Segel equation. We finally employ a purely semigroup analysis to prove linear, and then nonlinear, exponential stability of the system in appropriated functional spaces with polynomial weights.
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On the self-similar stability of the parabolic-parabolic Keller-Segel equation
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Autor/in / Beteiligte Person: | Borges, Frank Alvarez ; Carrapatoso, Kleber ; Mischler, Stéphane ; CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) ; Université Paris Dauphine-PSL ; Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) ; Centre de Mathématiques Laurent Schwartz (CMLS) ; École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS) |
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Zeitschrift: | https://hal.science/hal-04267741 ; 2023, 2023 |
Veröffentlichung: | HAL CCSD, 2023 |
Medientyp: | report |
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