【摘要】 讨论考虑热效应时半导体器件中电子电流、空穴电流和静电位等载流子运动的数学模型 ,这是一个非线性抛物椭圆型耦合偏微分方程组的混合初边值问题 .在假定初值n0 (x) ,p0 (x) ∈L∞+(Ω) ,边值n ,p ,θ∈H1 (Ω) ∩L∞+(Ω) ,ψ∈W1 ,3(Ω) ∩L∞+(Ω)等正则性条件下 ,利用先验估计、紧性原理和Schauder不动点定理 ,证明了弱解的整体存在性 .更多还原

【Abstract】 A mathematical model arising in semiconductor device, which describes the transport of carriers such as current of electrons, current of holes and electrostatic potential in the device with heat effect, is considered. The model is a coupled nonlinear partial differential equation system of parabolic elliptic type subject to mixed initial boundary values. We prove the global existence of the weak solution under appropriate regularity conditions such as initial values n 0(x),p 0(x)∈L ∞ +(Ω), boundary values n,p,θ∈H 1(Ω)∩L ∞ +(Ω),ψ∈W 1,3 (Ω)∩L ∞ +(Ω) by means of a priori estimates, compactness principle and Schauder fixed point theory.更多还原