WorkshopsNew Poisson-Boltzmann type equations (1)
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Continuing our previous work for ionic solutions with two ion species of opposite charges [Nonlinearity, 24 (2011) 431-458], we study a new Poisson-Boltzmann type (PB_n) equation which describes the equilibrium of electrolytes with multiple types of ionic species. Under Robin type boundary conditions with various material coefficients, we give the rigorous proof of the asymptotic behavior of the solutions of PB n equations in one spatial dimensional cases, as the parameter approaches zero. When the global electro-neutrality holds, we find different asypmtotic behaviors between PB_n and the standard Poisson-Boltzmann (PB) equations. Results for high dimensional domains and PB with finite size effects are also introduced.
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Chiun-Chang Lee
2012-01-06
15:30:00 - 15:55:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
Continuing our previous work for ionic solutions with two ion species of opposite charges [Nonlinearity, 24 (2011) 431-458], we study a new Poisson-Boltzmann type (PB_n) equation which describes the equilibrium of electrolytes with multiple types of ionic species. Under Robin type boundary conditions with various material coefficients, we give the rigorous proof of the asymptotic behavior of the solutions of PB n equations in one spatial dimensional cases, as the parameter approaches zero. When the global electro-neutrality holds, we find different asypmtotic behaviors between PB_n and the standard Poisson-Boltzmann (PB) equations. Results for high dimensional domains and PB with finite size effects are also introduced.