Asymptotic behavior of subsonic entropy solutions of the isentropic Euler-Poisson equations

Li, Hailiang; Markowich, Peter; Mei, Ming

doi:10.1090/qam/1939010

Authors: Hailiang Li, Peter Markowich and Ming Mei
Journal: Quart. Appl. Math. 60 (2002), 773-796
MSC: Primary 35L60; Secondary 35B40, 35L45, 35L67, 76X05
DOI: https://doi.org/10.1090/qam/1939010
MathSciNet review: MR1939010
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Abstract: The hydrodynamic model for semiconductors in one dimension is considered. For perturbated Riemann data, global subsonic (weak) entropy solutions, piecewise continuous and piecewise smooth solutions with shock discontinuities are constructed and their asymptotic behavior is analyzed. In subsonic domains, the solution is smooth and, exponentially as $t \to \infty$, tends to the corresponding stationary solution due to the influence of Poisson coupling. Along the shock discontinuity, the shock strength and the difference of derivatives of solutions decay exponentially affected by the relaxation mechanism.

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