S. Junca and M. Rascle, Relaxation of the isothermal Euler-Poisson system to the drift-di#usion equations, Quart. Appl. Math. 58 (2000), 511-521.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... from local existence in the small H neighborhood of a steady state [18, 23, 9] to global existence of weak solutions with geometrical symmetry [5] for the two carrier types in one dimension [29] the relaxation limit for the weak entropy solution, consult [21] for isentropic case, and [14] for isothermal case. For the question of global behavior of strong solutions, however, the choice of the initial data and or damping forces is decisive. The non existence results in the case of attractive forces, k 0, have been obtained by Makino Perthame [20] and for repulsive forces by ....

S. Junca and M. Rascle, Relaxation of the isothermal Euler-Poisson system to the drift-di#usion equations, Quart. Appl. Math. 58 (2000), 511-521.

.... problems, from local existence in the small HS neighborhood of a steady state [16, 21, 8] to global existence of real solutions with geometrical symmetry [5] for the two carrier types in one dimension [26] the relaxation limit for the weak entropy solution, consult [19] for isentropic case, and [14] for isothermal case. For the question of global behavior of strong solutions, however, the choice of the initial data and or damping forces is decisive. The non existence results in the case of attractive forces have been obtained by Makino Perthame [18] and for repulsive forces by Perthame ....

S. JUNCA AND M. RASCLE, Relaxation of the isothermal Euler-Poisson system to the drift-diffusion equations, Quart. Appl. Math. 58 (2000), 511-521.

....(usually, electrons and positively charged ions) by performing various asymptotic limits in which a small parameter tends to zero. The limit of vanishing (scaled) relaxation time and, under some conditions, the limit of vanishing (scaled) electron mass has been performed [11, 20, 22] also see [2, 3, 18, 31]) The limit of vanishing Debye length (the so called quasineutral limit) has been studied by Cordier and Grenier for the transient model [6] and by Slemrod and Sternberg for the stationary equations [35] A combined relaxation quasineutral limit has been performed by Gasser and Marcati [9] ....

S. Junca and M. Rascle, Relaxation of the isothermal Euler-Poisson system to the drift-diusion equations, Quart. Appl. Math. 58 (2000), 511-521.

....L 1 bounds. If the momentum and energy relaxation times are of the same order, but the mean free path is much smaller than the typical device length, we obtain formally the drift di usion equations from the hydrodynamic model. This limit has been shown rigorously for constant temperature in [22]. The asymptotic limit in the full model has been studied under some conditions in [1, 12] For an overview of these limits, see [23] The main objectives of this paper are rst to adopt the recently developed discrete BGK scheme [4] in order to solve numerically the hydrodynamic model in one ....

S. Junca and M. Rascle. Relaxation of the isothermal Euler-Poisson system to the drift-diusion equations. Quart. Appl. Math., 58:511-521, 2000.

.... from local existence in the small H s neighborhood of a steady state [16, 21, 8] to global existence of real solutions with geometrical symmetry [5] for the two carrier types in one dimension [26] the relaxation limit for the weak entropy solution, consult [19] for isentropic case, and [14] for isothermal case. For the question of global behavior of strong solutions, however, the choice of the initial data and or damping forces is decisive. The non existence results in the case of attractive forces have been obtained by Makino Perthame [18] and for repulsive forces by Perthame ....

S. Junca and M. Rascle, Relaxation of the isothermal Euler-Poisson system to the drift-diusion equations, Quart. Appl. Math. 58 (2000), 511-521.

.... whole sequence (N ; J ; converges since there is no general uniqueness result for the limiting problem (DD I) or (DD EI) The uniqueness question of these models is addressed to in, e.g. 14, 24] The relaxation limit for isothermal plasmas has been carried out by Junca and Rascle in [20, 21]. They consider a plasma consisting only of ions. The proof of their result is based on an entropy inequality and the de la Vall ee Poisson lemma. Notice that here, L 1 weak convergence of the particle density is enough to pass to the limit in the linear pressure term. The rst mathematical ....

S. Junca and M. Rascle. Relaxation of the isothermal Euler-Poisson system to the drift-diusion equations. To appear in Quart. Appl. Math., 2000.

....equations. Formally, we obtain (20) from (7) by assuming isentropic states and by neglecting t J n and the convective term q 1 div (J n J n =n) More rigorously, the isentropic drift di usion model can be derived from the isentropic hydrodynamic equations in 9 the zero relaxation time limit [45, 112, 124, 125, 139, 140, 141, 159, 162, 172, 189]. Another derivation starts from the transport equations J n = q 0 nr n ; J p = q 0 pr p ; 26) where the carrier densities are given by Fermi Dirac statistics [28, 82, 130] n = N c F 1=2 0 D 0 ( n V E c q ) p = N v F 1=2 0 D 0 ( p V E v q ) Here, ....

.... model in the formulation (19) for the electron current density) we directly get (27) Similar as for the isentropic drift di usion model, the standard drift di usion equations can be derived from the hydrodynamic model (6) 8) or the energy transport model) in the zero relaxation time limit [99, 124]. Finally, the standard model can be obtained directly from the Boltzmann equation by using the Hilbert expansion method [163, 183] More general drift di usion models than presented here have been derived; see, e.g. 34, 61, 103] 6. Quantum models For ultra small electronic devices in which ....

S. Junca and M. Rascle. Relaxation of the isothermal Euler-Poisson system to the drift-diusion equations. To appear in Quart. Appl. Math., 1999.

.... xx Phi = N i Gamma f ( Phi) 17) which yields, after letting formally 0; t N i Gamma x ( x p i (N i ) N i x Phi) 0; 18) Gamma xx Phi = N i Gamma f ( Phi) 19) The zero relaxation time limit in the hydrodynamic equations (9) 11) for isothermal plasmas has been proved in [5]. For adiabatic plasmas, this limit has been obtained in [8] under the assumption of given uniform L 1 estimates. The authors proved in [6] rigorously the zero relaxation time limit for adiabatic plasmas under the two (main) assumptions: H1) f 2 C 1 ( 0; 1) f(0) 0; f 0 (s) f 0 0 for ....

S. Junca and M. Rascle. Relaxation of the isothermal Euler-Poisson system to the drift-diffusion equations. To appear in Quart. Appl. Math., 1998.

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