A new proof of global existence of large solutions for the Poisson-Nernst-Planck equations
Purposes—To study the Poisson-Nernst-Planck equations arising from the semiconduc-tor theory,which describes the drift and diffusion phenomena of the charged particles,and to estab-lish the global existence of large solutions to this equations.Methods—Weighted method,perturba-tion method and contradiction method were used.Results—By introducing a new weighted function,we establish the nonlinear estimates of the perturbed equations in the Chemin-Lerner mixed time-space spaces and obtain the global existence of large solutions to the Poisson-Nernst-Planck equations by contradiction method.Conclusion—The difference of two classes of charged particles plays more im-portant role in the well-posed theory of this equations.
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维普
