Xing, Jiasheng; Guo, Xiulan Asymptotic behavior of time-dependent solutions to semiconductor equations. (English) Zbl 0964.35159 Ann. Differ. Equations 14, No. 2, 339-345 (1998). 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 Keywords:semiconductor equations; time-dependent solution; steady-state solution PDFBibTeX XMLCite \textit{J. Xing} and \textit{X. Guo}, Ann. Differ. Equations 14, No. 2, 339--345 (1998; Zbl 0964.35159)