Multiplicity and concentration of solutions for a fractional Schrödinger–Poisson system with sign-changing potential

2021 ◽  
pp. 1-22
Author(s):  
Guofeng Che ◽  
Haibo Chen
Keyword(s):  
Poisson System ◽  
Concentration Of Solutions

scholarly journals Existence and concentration of solutions of Schrödinger–Poisson system

2017 ◽  
Vol 68 ◽  
pp. 8-12 ◽  
Author(s):  
Anmin Mao ◽  
Lijuan Yang ◽  
Aixia Qian ◽  
Shixia Luan
Keyword(s):  
Poisson System ◽  
Concentration Of Solutions

scholarly journals Observers of Vlasov-Poisson system

2020 ◽  
Vol 53 (2) ◽  
pp. 5946-5951
Author(s):  
Amadou Cisse ◽  
Mohamed Boutayeb
Keyword(s):  
Poisson System

Diffusion limit of a Boltzmann–Poisson system with nonlinear equilibrium state

2019 ◽  
Vol 16 (01) ◽  
pp. 131-156
Author(s):  
Lanoir Addala ◽  
Mohamed Lazhar Tayeb
Keyword(s):  
Nonlinear Diffusion ◽  
Collision Operator ◽  
Nonlinear Diffusion Equation ◽  
One Dimension ◽  
Diffusion Limit ◽  
Poisson System ◽  
Nonlinear Relaxation ◽  
Contraction Property ◽  
Hilbert Expansion ◽  
Nonlinear Equilibrium

The diffusion approximation for a Boltzmann–Poisson system is studied. Nonlinear relaxation type collision operator is considered. A relative entropy is used to prove useful [Formula: see text]-estimates for the weak solutions of the scaled Boltzmann equation (coupled to Poisson) and to prove the convergence of the solution toward the solution of a nonlinear diffusion equation coupled to Poisson. In one dimension, a hybrid Hilbert expansion and the contraction property of the operator allow to exhibit a convergence rate.

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