The charge conserving Poisson-Boltzmann equations: Existence, uniqueness, and maximum principle
Journal Article
·
· Journal of Mathematical Physics
- Department of Applied Mathematics, National Hsinchu University of Education, Hsinchu 300, Taiwan (China)
The present article is concerned with the charge conserving Poisson-Boltzmann (CCPB) equation in high-dimensional bounded smooth domains. The CCPB equation is a Poisson-Boltzmann type of equation with nonlocal coefficients. First, under the Robin boundary condition, we get the existence of weak solutions to this equation. The main approach is variational, based on minimization of a logarithm-type energy functional. To deal with the regularity of weak solutions, we establish a maximum modulus estimate for the standard Poisson-Boltzmann (PB) equation to show that weak solutions of the CCPB equation are essentially bounded. Then the classical solutions follow from the elliptic regularity theorem. Second, a maximum principle for the CCPB equation is established. In particular, we show that in the case of global electroneutrality, the solution achieves both its maximum and minimum values at the boundary. However, in the case of global non-electroneutrality, the solution may attain its maximum value at an interior point. In addition, under certain conditions on the boundary, we show that the global non-electroneutrality implies pointwise non-electroneutrality.
- OSTI ID:
- 22306212
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 5 Vol. 55; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
On long time asymptotics of the Vlasov-Poisson-Boltzmann equation
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Nonlinear Boltzmann equation with partially absorbing boundary conditions. Global existence and uniqueness results
Journal Article
·
Mon Dec 31 23:00:00 EST 1990
· Communications in Partial Differential Equations; (United States)
·
OSTI ID:5354948
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Journal Article
·
Wed Jan 06 23:00:00 EST 2016
· Journal of Chemical Physics
·
OSTI ID:22493612
Nonlinear Boltzmann equation with partially absorbing boundary conditions. Global existence and uniqueness results
Journal Article
·
Fri May 01 00:00:00 EDT 1987
· J. Math. Phys. (N.Y.); (United States)
·
OSTI ID:6680356