Hsiao, Ling; Wang, Shu Asymptotic behavior of global smooth solutions to the full 1D hydrodynamic model for semiconductors. (English) Zbl 1174.82349 Math. Models Methods Appl. Sci. 12, No. 6, 777-796 (2002). Summary: In this paper, we study the asymptotic behavior of smooth solutions to the initial boundary value problem for the full one-dimensional hydrodynamic model for semiconductors. We prove that the solution to the problem converges to the unique stationary solution time asymptotically exponentially fast. Cited in 11 Documents MSC: 82D37 Statistical mechanics of semiconductors 35B40 Asymptotic behavior of solutions to PDEs 35L60 First-order nonlinear hyperbolic equations 35L65 Hyperbolic conservation laws 35Q60 PDEs in connection with optics and electromagnetic theory 76X05 Ionized gas flow in electromagnetic fields; plasmic flow Keywords:Full hydrodynamic model; semiconductors; asymptotic behavior; global smooth solutions PDFBibTeX XMLCite \textit{L. Hsiao} and \textit{S. Wang}, Math. Models Methods Appl. Sci. 12, No. 6, 777--796 (2002; Zbl 1174.82349) Full Text: DOI References: [1] DOI: 10.1137/S0036141099355174 · Zbl 0984.35104 · doi:10.1137/S0036141099355174 [2] DOI: 10.1016/0893-9659(94)00104-K · Zbl 0817.76102 · doi:10.1016/0893-9659(94)00104-K [3] Cordier S., RAIRO Modél. Math. Anal. Numér. 32 pp 1– (1998) · Zbl 0935.35119 · doi:10.1051/m2an/1998320100011 [4] DOI: 10.1016/0893-9659(90)90130-4 · Zbl 0736.35129 · doi:10.1016/0893-9659(90)90130-4 [5] DOI: 10.1007/BF01765842 · Zbl 0808.35150 · doi:10.1007/BF01765842 [6] Gamba I. M., Comm. P.D.E. 17 pp 553– (1992) [7] Gasser I., Quarterly of Appl. Math. pp 269– (1999) · Zbl 1034.82067 · doi:10.1090/qam/1686190 [8] DOI: 10.1006/jdeq.1996.0034 · Zbl 0859.76067 · doi:10.1006/jdeq.1996.0034 [9] Junca S., Quart. Appl. Math. 58 pp 511– (2000) [10] DOI: 10.1137/S0036139996312168 · Zbl 0936.35111 · doi:10.1137/S0036139996312168 [11] DOI: 10.1017/S030821050003078X · Zbl 0831.35157 · doi:10.1017/S030821050003078X [12] DOI: 10.1007/BF00379918 · Zbl 0829.35128 · doi:10.1007/BF00379918 [13] DOI: 10.1007/BF00945711 · Zbl 0755.35138 · doi:10.1007/BF00945711 [14] DOI: 10.1016/S0362-546X(99)00168-6 · Zbl 0965.65113 · doi:10.1016/S0362-546X(99)00168-6 [15] DOI: 10.1006/jdeq.1995.1158 · Zbl 0845.35123 · doi:10.1006/jdeq.1995.1158 [16] DOI: 10.1007/BF02098016 · Zbl 0785.76053 · doi:10.1007/BF02098016 [17] 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.