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• W2524533700 startingPage "3251" @default.
• W2524533700 abstract "Concerning the influence of the dielectric constant on the electrostatic potential in the bulk ofelectrolyte solutions, we investigate a charge conserving Poisson-Boltzmann (CCPB) equation [31,32]with a variable dielectric coefficient and a small parameter $epsilon$(related to the Debye screening length) in a bounded connected domain with smooth boundary.Under the Robin boundary condition with a given applied potential,the limiting behavior (as $epsilondownarrow0$) of the solution (the electrostatic potential) has been rigorously studied. In particular,under the charge neutrality constraint,our result exactly shows the effects of the dielectric coefficient and the applied potential on the limiting value of the solution in the interior domain.The main approach is the Pohozaev's identity of this model.On the other hand, under the charge non-neutrality constraint,we show thatthe maximum difference between the boundary and interior values of the solutionhas a lower bound $logfrac{1}{epsilon}$ as $epsilon$ goes to zero.Such an asymptotic blow-up behaviordescribes an unstable phenomenonwhich is totally different from the behavior of the solutionunder the charge neutrality constraint." @default.
• W2524533700 created "2016-10-07" @default.
• W2524533700 creator A5008420963 @default.
• W2524533700 date "2015-12-01" @default.
• W2524533700 modified "2023-09-24" @default.
• W2524533700 title "Asymptotic analysis of charge conserving Poisson-Boltzmann equations with variable dielectric coefficients" @default.
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• W2524533700 doi "https://doi.org/10.3934/dcds.2016.36.3251" @default.
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