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Asymptotic behavior of time-dependent solutions to semiconductor equations. (English) Zbl 0964.35159

Summary: This paper considers the relationship between the time-dependent solutions and the steady-state solutions to the semiconductor equations \[ {\partial u_i\over\partial t}- \text{div }J_i= -R(u),\quad i= 1,2, \]
\[ -\nabla(a\nabla \psi)= f+ u_2- u_1, \]
\[ (u_i,\psi)|_{\Gamma_D}= (\overline u_i, \overline\psi),\quad J_i\cdot\nu|_{\Gamma_N}= {\partial\psi\over\partial\nu} \Biggl|_{\Gamma_N}= 0, \]
\[ u_i(0)= u_{0i}(x),\quad x\in G, \] under thermal equilibrium conditions. The asymptotic behavior of the time-dependent solution is obtained.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
78A35 Motion of charged particles
82D37 Statistical mechanics of semiconductors
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