Large-time behavior of solutions to Cauchy problem for bipolar Euler–Poisson system with time-dependent damping in critical case Article Swipe

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Euler's formula Poisson distribution Cauchy problem Mathematics Mathematical analysis Initial value problem Euler system Cauchy distribution Applied mathematics Physics Euler equations Statistics

Liping Luan , Ming Mei , Bruno Rubino , Peicheng Zhu ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.4310/cms.2021.v19.n5.a2 · OA: W3181388005

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.