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In this paper, considering the existence and large time behavior of the overall solution of the initial value problem in one-dimensional space . Where ρ n is the electron density and the hole density , E is the electric field , the pressure function p ( ρ ) = the ρ m < / sup >, P ( n ) = n m < / SUP > ( m gt; 1), ε gt; 0 metrizable (scaled) Planck constant , ρ ± is given constant . Definition which W is one dimensional quasi linear parabolic equations ρ t = ( ρ m < / sup >) xx ( m gt; 1 ) self-similar solution (Ref. [ 19 ] ) and , x 0 meet the following main conclusions we can get . Theorem If ρ 0 < / sub > gt ; 0, n 0 < / sub > gt ; 0, ( g 0 h 0 ) ∈ H 3 × H 3 , ‖ g 0 < / sub > ‖ H 3 (R ) ‖ h 0 < / sub> sufficiently small ‖ H 3 (R) and | ρ is the -ρ - < / sub > | lt; lt ; 1 , the initial value problem (1) has a unique global strong solution ( ρ , n, E ) . Further, when the time goes to infinity , the initial value problem (1) Solution ρ n asymptotic convergence W, and satisfies : wherein C, β is a normal number .
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