In this paper, we study the global existence and the global nonexistence of doubly nonlinear degenerate parabolic systems with nonlinear boundary conditions. We first prove a local existence result by the regularization method. Next, we construct a weak comparison principle. Then we discuss the large time behavior of solutions by using a modified upper and lower solution methods and constructing various upper and lower solutions. Necessary and sufficient conditions on the global existence of all positive (weak) solutions are obtained.

The quasineutral limit of Euler-Poisson system with and without viscosity in plasma physics in the torusΤd, d ≥ 1 is studied. That quasineutral regimes are the incompressible Euler or Navier-Stokes equations is proven. In the mean time, long-time existence for large amplitude smooth solutions of Euler-Poisson system in torus Τd, d ≥ 1, with or without viscosity as the Debye length λ→ 0 is also obtained provided that the smooth solution of incompressible Euler or Navier-Stokes equations exists globally for nearby initial data. In particular, the existence of large amplitude smooth solutions of Euler-Poisson system in torus Τ2 with or without viscosity and with sufficiently small Debye length is obtained on any arbitrary time interval. The proof of these results is based on a straightforward extension of the classical energy method, the modulated energy method, the iteration techniques and the standard compactness argument.

The limit for vanishing Debye length (charge neutral limit) in a bipolar drift-diffusion model for semiconductors with general initial data allowing the presence of an initial layer is studied. The quasineutral limit (zero-Debye-length limit) is performed rigorously by using two dierent entropy functionals which yield appropriate uniform estimates. This investigation extends the results of Refs. 7 and 8 for charge neutral initial data where no initial layer occurs

The combined semi-classical and quasineutral limit in the bipolar defocusing nonlinear Schr