双极量子流体动力学模型的混合边值问题

Mixed Boundary Value Problem of a Bipolar Quantum Hydrodynamic Model

研究了下列椭圆方程组的混合边值问题:δ2△u=2u(V+g1(u)△α1),δ2△w=w(-V+g2(w2)-α2),-λ2△V=u2-w2-C,u=u0,w=w0,V=V0 on ΓD,u/ν=w/ν=V/ν=0 on ΓN.这里u0,w0,V0∈H1(Ω)∩L∞(Ω),u0,w0≥0 in Ω,ν是ΓN上的单位外法向量.证明了方程组解的存在性和唯一性.

In this paper, we investigate the following mixed boundary value problem of an elliptic systems： δ^2Δu = u（V ＋ g1（u^2）-α1）,δ^2Δw = w（-V ＋ g2（w^2）-α2 ）- λ^2ΔV = u^2 - w^2 - C,u=u0,w-w0,V =V0, on ΓD,δu/δv=δw/δv=δV/δv=0,on ΓN, where uo,wo,Vo∈H^1（Ω）∩L^∞（Ω）, u0,w0≥0, in Ω , V is the unit outward normal to ΓN. We prove the existence and uniqueness of the solution of the system.