Hsiao, Ling; Zhang, Kaijun The global weak solution and relaxation limits of the initial-boundary value problem to the bipolar hydrodynamic model for semiconductors. (English) Zbl 1174.82350 Math. Models Methods Appl. Sci. 10, No. 9, 1333-1361 (2000). Summary: The convergence and consistency of approximate solutions derived by the modified Godunov scheme for the initial-boundary value problem to a bipolar hydrodynamic model for semiconductors are proved using the compensated compactness framework. The information of weak solutions to satisfy the boundary conditions is also displayed. The zero relaxation limit of the bipolar hydrodynamic model towards the drift-diffusion model is carried out when the current relaxation time tends to zero. Cited in 1 ReviewCited in 30 Documents MSC: 82D37 Statistical mechanics of semiconductors 35L65 Hyperbolic conservation laws PDFBibTeX XMLCite \textit{L. Hsiao} and \textit{K. Zhang}, Math. Models Methods Appl. Sci. 10, No. 9, 1333--1361 (2000; Zbl 1174.82350) Full Text: DOI References: [1] DOI: 10.1063/1.531567 · Zbl 0868.45006 · doi:10.1063/1.531567 [2] DOI: 10.1007/BF02179583 · Zbl 1081.82610 · doi:10.1007/BF02179583 [3] DOI: 10.1109/T-ED.1970.16921 · doi:10.1109/T-ED.1970.16921 [4] Chen G.-Q., Acta. Math. Sci. 6 pp 75– (1986) [5] DOI: 10.1002/cpa.3160460504 · Zbl 0797.35113 · doi:10.1002/cpa.3160460504 [6] DOI: 10.1002/cpa.3160470602 · Zbl 0806.35112 · doi:10.1002/cpa.3160470602 [7] DOI: 10.1016/0893-9659(94)00104-K · Zbl 0817.76102 · doi:10.1016/0893-9659(94)00104-K [8] DOI: 10.1512/iumj.1982.31.31039 · Zbl 0497.35058 · doi:10.1512/iumj.1982.31.31039 [9] DOI: 10.1016/0893-9659(90)90130-4 · Zbl 0736.35129 · doi:10.1016/0893-9659(90)90130-4 [10] DOI: 10.1007/BF01765842 · Zbl 0808.35150 · doi:10.1007/BF01765842 [11] Ding X., Acta Math. Sci. 5 pp 415– (1985) [12] Ding X., Acta Math. Sci. 5 pp 433– (1985) [13] DOI: 10.1007/BF01218624 · Zbl 0689.76022 · doi:10.1007/BF01218624 [14] DOI: 10.1007/BF01206047 · Zbl 0533.76071 · doi:10.1007/BF01206047 [15] DOI: 10.1007/BF00251724 · Zbl 0519.35054 · doi:10.1007/BF00251724 [16] DOI: 10.1006/jdeq.1996.3203 · Zbl 0884.34031 · doi:10.1006/jdeq.1996.3203 [17] Gamba I. M., Comm. Partial Differential Equations 17 pp 553– (1992) [18] Golse F., Asymptotic Anal. 6 pp 135– (1992) [19] DOI: 10.1007/BF00380896 · Zbl 0812.35076 · doi:10.1007/BF00380896 [20] Hsiao L., Ann. Scuola Norm. Sup. Pisa Cl. Sci. IV 15 pp 65– (1988) [21] DOI: 10.1137/0145034 · Zbl 0611.35026 · doi:10.1137/0145034 [22] DOI: 10.1142/S0218202594000388 · Zbl 0820.35128 · doi:10.1142/S0218202594000388 [23] DOI: 10.1142/S0218202595000292 · Zbl 0841.35114 · doi:10.1142/S0218202595000292 [24] DOI: 10.1080/03605309908821456 · Zbl 0946.35074 · doi:10.1080/03605309908821456 [25] DOI: 10.1007/BF02102014 · Zbl 0799.35151 · doi:10.1007/BF02102014 [26] Lions P. L., Comm. Pure Appl. Math. 44 pp 599– (1996) [27] DOI: 10.1016/0022-0396(90)90130-H · Zbl 0715.35065 · doi:10.1016/0022-0396(90)90130-H [28] DOI: 10.1017/S030821050003078X · Zbl 0831.35157 · doi:10.1017/S030821050003078X [29] DOI: 10.1007/BF00379918 · Zbl 0829.35128 · doi:10.1007/BF00379918 [30] Markowich P. A., Z. Angew. Math. Phys. 62 pp 389– [31] DOI: 10.1137/0144018 · Zbl 0559.34058 · doi:10.1137/0144018 [32] DOI: 10.1006/jmaa.1996.0081 · Zbl 0889.35109 · doi:10.1006/jmaa.1996.0081 [33] DOI: 10.1016/0022-0396(77)90129-2 · Zbl 0303.35052 · doi:10.1016/0022-0396(77)90129-2 [34] DOI: 10.1137/0150094 · Zbl 0724.35104 · doi:10.1137/0150094 [35] Poupaud F., Asymptotic Anal. 4 pp 293– (1991) [36] DOI: 10.1006/jdeq.1995.1158 · Zbl 0845.35123 · doi:10.1006/jdeq.1995.1158 [37] DOI: 10.1002/j.1538-7305.1950.tb03653.x · Zbl 1372.35295 · doi:10.1002/j.1538-7305.1950.tb03653.x [38] DOI: 10.1002/cpa.3160330502 · Zbl 0424.35057 · doi:10.1002/cpa.3160330502 [39] DOI: 10.1016/0022-247X(80)90159-6 · Zbl 0457.35058 · doi:10.1016/0022-247X(80)90159-6 [40] DOI: 10.1007/BF02098016 · Zbl 0785.76053 · doi:10.1007/BF02098016 [41] Zhang K. J., J. Partial Differential Equations 12 pp 369– (1999) [42] DOI: 10.1006/jdeq.1997.3381 · Zbl 0913.35060 · doi:10.1006/jdeq.1997.3381 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.