Optimal convergence rate to nonlinear diffusion waves for bipolar Euler–Poisson equations with critical overdamping

References

• Markowich PA, Ringhofer CA, Schmeiser C. Semiconductor equations. Berlin: Springer Verlag; 1990.
   Google Scholar
• Sitenko A, Malnev V. Plasma physics theory. London: Chapman & Hall; 1995. (Appl. Math. Math. Comput.; 10).
   Google Scholar
• Gasser I, Hsiao L, Li HL. Large time behavior of solutions of the bipolar hydrodynamic model for semiconductors. J Differ Equ. 2003;192:326–359.
   Web of Science ®Google Scholar
• Huang FM, Li YP. Large time behavior and quasineutral limit of solutions to a bipolar hydrodynamic model with large data and vacuum. Discrete Contin Dyn Syst. 2009;24:455–470.
   Web of Science ®Google Scholar
• Huang FM, Mei M, Wang Y. Large time behavior of solutions to n-dimensional bipolar hydrodynamic models for semiconductors. SIAM J Math Anal. 2011;43:1595–1630.
   Web of Science ®Google Scholar
• Li HT, Li JY, Mei M, et al. Asymptotic behavior of solutions to bipolar Euler–Poisson equations with time-dependent damping. J Math Anal Appl. 2019;437:1081–1121.
   Google Scholar
• Luan LP, Mei M, Rubino B, et al. Large-time behavior of solutions to Cauchy problem for bipolar Euler–Poisson system with time-dependent damping in critical case. Commun Math Sci. 2021;19:1207–1231.
   Web of Science ®Google Scholar
• Hsiao L, Liu TP. Convergence to diffusion waves for solutions of a system of hyperbolic conservation laws with damping. Commun Math Phys. 1992;259:599–605.
   Google Scholar
• Chen SH, Li HT, Li JY, et al. Global and blow-up solutions for compressible Euler equations with time-dependent damping. J Differ Equ. 2020;268:5035–5077.
   Web of Science ®Google Scholar
• Cui HB, Yin HY, Zhang JS, et al. Convergence to nonlinear diffusion waves for solutions of Euler equations with time-depending damping. J Differ Equ. 2018;264:4564–4602.
   Web of Science ®Google Scholar
• Geng SF, Lin YP, Mei M. Asymptotic behavior of solutions to Euler equations with time-dependent damping in critical case. SIAM J Math Anal. 2020;52:1463–1488.
   Web of Science ®Google Scholar
• Hou F, Witt I, Yin HC. Global existence and blowup of smooth solutions of 3-D potential equations with time-dependent damping. Pacific J Math. 2018;292:389–426.
   Web of Science ®Google Scholar
• Hou F, Yin HC. On the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping. Nonlinearity. 2017;30:2485–2517.
   Web of Science ®Google Scholar
• Ji SM, Mei M. Optimal decay rates of the compressible Euler equations with time-dependent damping in Rn: (I) under-damping case, preprint, 2020.
   Google Scholar
• Ji SM, Mei M. Optimal decay rates of the compressible Euler equations with time-dependent damping in Rn: (II) over-damping case, preprint, 2020.
   Google Scholar
• Li HT, Li JY, Mei M, et al. Convergence to nonlinear diffusion waves for solutions of p-system with time-dependent damping. J Math Anal Appl. 2017;456:849–871.
   Web of Science ®Google Scholar
• Li HT, Li JY, Mei M, et al. Optimal convergence rate to nonlinear diffusion waves for Euler equations with cirical overdamping. Appl Math Lett. 2021;113:106882.
   Google Scholar
• Mei M. Best asymptotic profile for hyperbolic p-system with damping. SIAM J Math Anal. 2010;42:1–23.
   Web of Science ®Google Scholar
• Nishihara K. Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping. J Differ Equ. 1996;131:171–188.
   Web of Science ®Google Scholar
• Nishihara K, Wang W, Yang T. Lp-convergence rates to nonlinear diffusion waves for p-system with damping. J Differ Equ. 2000;161:191–218.
   Web of Science ®Google Scholar
• Pan XH. Global existence of solutions to 1-d Euler equations with time-dependent damping. Nonlinear Anal. 2016;132:327–336.
   Web of Science ®Google Scholar
• Pan XH. Blow up of solutions to 1-d Euler equations with time-dependent damping. J Math Anal Appl. 2016;442:435–445.
   Web of Science ®Google Scholar
• Pan XH. Global existence and asymptotic behavior of solutions to the Euler equations with time-dependent damping. Applicable Anal. 2020;100:1–30.
   Web of Science ®Google Scholar
• Sideris T, Thomases B, Wang D. Long time behavior of solutions to the 3D compressible Euler equations with damping. Commun Partial Differ Equ. 2003;28:795–816.
   Web of Science ®Google Scholar
• Sugiyama Y. Singularity formation for the 1-D compressible Euler equations with variable damping coefficient. Nonlinear Anal. 2018;170:70–87.
   Web of Science ®Google Scholar
• Huang FM, Mei M, Wang Y, et al. Asymptotic convergence to stationary waves for unipolar hydrodynamic model of semiconductors. SIAM J Math Anal. 2011;43:411–429.
   Web of Science ®Google Scholar
• Li HL, Markowich PA, Mei M. Asymptotic behaviour of solutions of the hydrodynamic model of semiconductor. Proc R Soc Edinburgh Sect A. 2002;132:359–378.
   Web of Science ®Google Scholar
• Luo T, Natalini R, Xin Z. Large time behavior of the solutions to a hydrodynamic model for semiconductors. SIAM J Appl Math. 1998;59:810–830.
   Web of Science ®Google Scholar
• Matsumura A, Murakami T. Asymptotic behavior of solutions for a fluid dynamical model of semiconductor equation. Kyoto Univ RIMS Kokyuroku. 2006;1495:60–70.
   Google Scholar
• Nishibata S, Suzuki M. Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors. Osaka J Math. 2007;44:639–665.
   Web of Science ®Google Scholar
• Nishibata S, Suzuki M. Asymptotic stability of a stationary solution to a thermal hydrodynamic model for semiconductors. Arch Ration Mech Anal. 2009;192:187–215.
   Web of Science ®Google Scholar
• Zhu C, Hattori H. Stability of steady state solutions for an isenropic hydrodynamic model of semiconductors of two species. J Differ Equ. 2000;166:1–32.
   Web of Science ®Google Scholar
• van Duyn CJ, Peletier LA. A class of similarity solutions of the nonlinear diffusion equation. Nonlinear Anal. 1977;1:223–233.
   Google Scholar
• Matsumura A. Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equation with the first-order dissipation. Publ RIMS Kyoto Univ. 1977;13:349–379.
   Google Scholar