The Cauchy problem for the Vlasov-Maxwell equations
Glassey, Robert T., Schaeffer, Jack (1989)
Portugaliae mathematica
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Glassey, Robert T., Schaeffer, Jack (1989)
Portugaliae mathematica
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Jinn-Liang Liu, Dexuan Xie, Bob Eisenberg (2017)
Molecular Based Mathematical Biology
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We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation...
Gerhard Rein (1997)
Banach Center Publications
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We give a review of results on the initial value problem for the Vlasov--Poisson system, concentrating on the main ingredients in the proof of global existence of classical solutions.
François Golse (2001-2002)
Séminaire Équations aux dérivées partielles
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This paper discusses two new directions in velocity averaging. One is an improvement of the known velocity averaging results for functions. The other shows how to adapt some of the ideas of velocity averaging to a situation that is essentially a new formulation of the Vlasov-Maxwell system.
Weihua Geng (2015)
Molecular Based Mathematical Biology
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Numerically solving the Poisson-Boltzmann equation is a challenging task due to the existence of the dielectric interface, singular partial charges representing the biomolecule, discontinuity of the electrostatic field, infinite simulation domains, etc. Boundary integral formulation of the Poisson-Boltzmann equation can circumvent these numerical challenges and meanwhile conveniently use the fast numerical algorithms and the latest high performance computers to achieve combined improvement...
Robert Stańczy (2008)
Banach Center Publications
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The existence of steady states in the microcanonical case for a system describing the interaction of gravitationally attracting particles with a self-similar pressure term is proved. The system generalizes the Smoluchowski-Poisson equation. The presented theory covers the case of the model with diffusion that obeys the Fermi-Dirac statistic.
Philippe H. Droz-Vincent (1967)
Annales de l'I.H.P. Physique théorique
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