## On existence, uniqueness and asymptotic behavior of solutions of the basic equations for carrier transport in semiconductors.(English)Zbl 0579.35016

This work is concerned with global existence, uniqueness and asymptotic behaviour of solutions to the boundary value problem $-\Delta u=\epsilon^{-1}q(f+p-n)\quad in\quad (0,T)\times G;\quad qn_ t=\nabla \cdot j_ n-qR,\quad j_ n=q(D_ n\nabla n-\mu p\nabla u)$
$q\frac{\partial p}{\partial t}=-\nabla \cdot j_ p-qR,\quad j_ p=- q(D_ p\nabla p+\mu p\nabla u);\quad u=u_ s,\quad n=n_ s,\quad p=p_ s\quad in\quad (0,T)\times S_ 1$
$\frac{\partial u}{\partial \nu}+\alpha u=u_ s,\quad \nu \cdot j_ n=\nu j_ p=0\quad in\quad (0,T)\times S_ 2;\quad n(0,x)=n_ 0(x),\quad p(0,x)=p_ 0(x)\quad in\quad G$ which serves as model of mobile carrier transport in semiconductors. The proof relies on global a priori estimates obtained from the monotonicity of a certain Lyapunov function.
Reviewer: V.Barbu

### MSC:

 35G20 Nonlinear higher-order PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B40 Asymptotic behavior of solutions to PDEs 35Q99 Partial differential equations of mathematical physics and other areas of application
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### References:

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