Stability of the Front under a Vlasov-Fokker-Planck Dynamics
被引:16
作者:
Esposito, R.
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机构:
Univ Aquila, Dipartimento Matemat, I-67100 Coppito, AQ, ItalyUniv Aquila, Dipartimento Matemat, I-67100 Coppito, AQ, Italy
Esposito, R.
[1
]
Guo, Y.
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机构:
Brown Univ, Div Appl Math, Providence, RI 02812 USAUniv Aquila, Dipartimento Matemat, I-67100 Coppito, AQ, Italy
Guo, Y.
[2
]
Marra, R.
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机构:
Univ Roma Tor Vergata, Dipartimento Fis, I-00133 Rome, Italy
Univ Roma Tor Vergata, Unita INFN, I-00133 Rome, ItalyUniv Aquila, Dipartimento Matemat, I-67100 Coppito, AQ, Italy
Marra, R.
[3
,4
]
机构:
[1] Univ Aquila, Dipartimento Matemat, I-67100 Coppito, AQ, Italy
[2] Brown Univ, Div Appl Math, Providence, RI 02812 USA
[3] Univ Roma Tor Vergata, Dipartimento Fis, I-00133 Rome, Italy
[4] Univ Roma Tor Vergata, Unita INFN, I-00133 Rome, Italy
We consider a kinetic model for a system of two species of particles interacting through a long range repulsive potential and a reservoir at given temperature. The model is described by a set of two coupled Vlasov-Fokker-Plank equations. The important front solution, which represents the phase boundary, is a stationary solution on the real line with given asymptotic values at infinity. We prove the asymptotic stability of the front for small symmetric perturbations.