Luan, Liping; Mei, Ming; Rubino, Bruno; Zhu, Peicheng Large-time behavior of solutions to Cauchy problem for bipolar Euler-Poisson system with time-dependent damping in critical case. (English) Zbl 1479.35110 Commun. Math. Sci. 19, No. 5, 1207-1231 (2021). Summary: This paper is concerned with the Cauchy problem of a bipolar hydrodynamic model for semiconductor device, a system of one dimensional Euler-Poisson equations with time-dependent damping effect in the critical case. The global existence and uniqueness of the solutions to the Cauchy problem are proved by the technical time-weighted energy method, when the initial perturbation around the constant states are small enough. Particularly, the algebraic time-convergence-rates for the solutions to their constant states are also derived. Cited in 6 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35L45 Initial value problems for first-order hyperbolic systems 35L60 First-order nonlinear hyperbolic equations 35L67 Shocks and singularities for hyperbolic equations Keywords:Euler-Poisson equations; time-weighted energy method; global solutions; hydrodynamic model for semiconductor devices; one space dimension PDFBibTeX XMLCite \textit{L. Luan} et al., Commun. Math. Sci. 19, No. 5, 1207--1231 (2021; Zbl 1479.35110) Full Text: DOI