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Discontinuous Solutions for a Hydrodynamic Model of Semiconductors by Dening Li; Sixin Qian is a Mathematics article available to read on EtoBox.

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= H ± 1 (U ± \* ; ÿ \* ; (∇ÿ) \* ; (∇ ± ) \* ) in ± × [0; T ]; U ± \* ( x; 0) = U ± 0 \* ( x) in ± ; (u + \* ; v + \* ; w + \* ) • | @ ×[0;T ] = 0; G(U + \* ; U - \* ; ÿ \* ; @ t ÿ \* ; (∇ÿ) \* )| M0×[0;T ] where Then we use them to solve the initial-boundary value problem (4.2) -(4.5) to get (U ±; 1 \* ; ÿ 1 \* ). Then again by (4.1) we obtain (U ±; 1 ; ÿ 1 ). On the other hand, we start from (U ±; 0 ; ÿ 0 ) to solve the boundary value problem (4.6) -(4.9) to obtain ±; 1 . Once we get (U ±;k ; ÿ k ; ±;k ); we will compute (U ±;k \* ; ÿ k \* ; ±;k \* ) by (4.1). And then using (U ±;k \* ; ÿ k \* ; ±;k \* ); we solve (4.2) -(4.5) to get (U ±;k+1 \* ; ÿ k+1 \* ). Then again by (4.1), we obtain (U ±;k+1 ; ÿ k+1 ). By using (U ±;k ; ÿ k ) to solve (4.6) -(4.9), we will get ±;k+1 . Recall that we use Newton's iteration (4.5), i.e. \* -U ±; 0 \* , then U \* satisÿes where in (4.22) we have used estimate (4.11). with the boundary conditions similar to (4.7) -(4.9). Where in (4.22), C(U +; 0 \* ; U -; 0 \* ; ÿ 0 \* ; @ t ÿ 0 \* ; ) is a smooth matrix function of its arguments, the expression (V +;k \* ; V -;k \* ; k \* ; @ t k \* ) 2 is a simpliÿed notation for a quadratic function of all

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Author

Dening Li; Sixin Qian

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0362-546X)

Published

2002

Language

EN

Field

Mathematics (Physical Sciences)