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2005年03月29日

【期刊论文】Quasineutral Limit of Euler-Poisson System with and without Viscosity

王术， Shu Wang* #

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS Vol. 29, Nos. 3 & 4, pp. 419-456, 2004，-0001，（）：

-1年11月30日

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.

Euler-Poisson system， Viscosity， Incompressible Euler equations， Incompressible Navier-Stokes equations， Quasineutral limit.，

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2005年03月29日

【期刊论文】Quasilinear Parabolic Systems with Nonlinear Boundary Conditions

王术， Shu Wang， Mingxin Wang， Chunhong Xie

Journal of Differential Equations 166, 251-265 (2000)，-0001，（）：

-1年11月30日

摘要

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2005年03月29日

【期刊论文】CONVERGENCE OF NONLINEAR SCHR

王术， Ansgar J

，-0001，（）：

-1年11月30日

摘要

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

Bipolar defocusing nonlinear Schr

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2005年03月29日

【期刊论文】A nonlinear degenerate diffusion equation not in divergence form

王术， Wang Shu， Wang Mingxin and Xie Chun-hong

Z. angew. Math. Phys. 51(2000)149-159，-0001，（）：

-1年11月30日

摘要

We consider positive solution of the nonlinear degenerate diusion equation ut=up (△u+u) with Dirichlet boundary condition and p>1. It is proved that all positive solutions exist globally if and only if λ1≥1, where λ1 is the rst eigenvalue of −△on Ω with homogeneous Dirichlet boundary condition.

Degenerate diffusion equation,， global solution,， blow up,， upper and lower solutions method.，